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Perturbed Semi-Markov Type Processes I

Perturbed Semi-Markov Type Processes I

Dmitrii Silvestrov

Springer Nature Switzerland AG
2022
sidottu
This book is the first volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation. The first volume presents necessary and sufficient conditions for weak convergence for first-rare-event times and convergence in the topology J for first-rare-event processes defined on regularly perturbed finite Markov chains and semi-Markov processes. The text introduces new asymptotic recurrent algorithms of phase space reduction. It also addresses both effective conditions of weak convergence for distributions of hitting times as well as convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes. The book also contains a comprehensive bibliography of major works in the field. It provides an effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications.
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Perturbed Semi-Markov Type Processes I

Perturbed Semi-Markov Type Processes I

Dmitrii Silvestrov

Springer Nature Switzerland AG
2023
nidottu
This book is the first volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation. The first volume presents necessary and sufficient conditions for weak convergence for first-rare-event times and convergence in the topology J for first-rare-event processes defined on regularly perturbed finite Markov chains and semi-Markov processes. The text introduces new asymptotic recurrent algorithms of phase space reduction. It also addresses both effective conditions of weak convergence for distributions of hitting times as well as convergence of expectations of hitting times for regularly and singularly perturbed finite Markov chains and semi-Markov processes. The book also contains a comprehensive bibliography of major works in the field. It provides an effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications.
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Markov Decision Processes and Stochastic Positional Games

Markov Decision Processes and Stochastic Positional Games

Dmitrii Lozovanu; Stefan Wolfgang Pickl

Springer International Publishing AG
2024
sidottu
This book presents recent findings and results concerning the solutions of especially finite state-space Markov decision problems and determining Nash equilibria for related stochastic games with average and total expected discounted reward payoffs. In addition, it focuses on a new class of stochastic games: stochastic positional games that extend and generalize the classic deterministic positional games. It presents new algorithmic results on the suitable implementation of quasi-monotonic programming techniques. Moreover, the book presents applications of positional games within a class of multi-objective discrete control problems and hierarchical control problems on networks. Given its scope, the book will benefit all researchers and graduate students who are interested in Markov theory, control theory, optimization and games.
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Markov Decision Processes and Stochastic Positional Games

Markov Decision Processes and Stochastic Positional Games

Dmitrii Lozovanu; Stefan Wolfgang Pickl

Springer International Publishing AG
2025
nidottu
This book presents recent findings and results concerning the solutions of especially finite state-space Markov decision problems and determining Nash equilibria for related stochastic games with average and total expected discounted reward payoffs. In addition, it focuses on a new class of stochastic games: stochastic positional games that extend and generalize the classic deterministic positional games. It presents new algorithmic results on the suitable implementation of quasi-monotonic programming techniques. Moreover, the book presents applications of positional games within a class of multi-objective discrete control problems and hierarchical control problems on networks. Given its scope, the book will benefit all researchers and graduate students who are interested in Markov theory, control theory, optimization and games.
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Mathematical Modelling by Help of Category Theory

Mathematical Modelling by Help of Category Theory

Dmitrii Legatiuk

Springer International Publishing AG
2025
sidottu
This monograph offers a novel structural perspective on the modelling of engineering problems, utilizing abstract mathematics in the form of category theory. Specifically, the book aims to enhance the understanding of mathematical modelling by developing a category theory-based framework. Category theory is employed to establish clear relationships between mathematical models and their complexities. The theory is then extended to encompass coupled mathematical models, incorporating more advanced categorical structures. To bridge theory and practice, the book presents engineering applications of the abstract categorical framework, providing various modelling examples from real-world engineering scenarios. Additionally, it introduces initial concepts for automatic model generation and error detection in modelling. The theory developed here demonstrates the practical utility of category theory, making this book a valuable resource for researchers in applied mathematics and engineering, particularly those focused on theoretical foundations of modelling.
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Coupling and Ergodic Theorems for Semi-Markov-Type Processes I

Coupling and Ergodic Theorems for Semi-Markov-Type Processes I

Dmitrii Silvestrov

Springer International Publishing AG
2025
sidottu
Ergodic theorems are a cornerstone of the theory of stochastic processes and their applications. This volume delves into ergodic theorems with explicit power and exponential upper bounds for convergence rates, focusing on Markov chains, renewal processes, and regenerative processes. The book offers a powerful and constructive probabilistic framework by employing the elegant coupling method in conjunction with test functions. Theoretical findings are illustrated with applications to perturbed stochastic networks, alternating Markov processes, risk processes, quasi-stationary distributions, and the renewal theorem, all of which feature explicit convergence rate bounds. Many results presented here are groundbreaking, appearing in publication for the first time. This is the first volume of a two-volume monograph dedicated to ergodic theorems. While this volume centers on Markovian and regenerative models, the second volume extends the scope to semi-Markov processes and multi-alternating regenerative processes with semi-Markov modulation. Designed with researchers and advanced students in mind, the content is thoughtfully structured by complexity, making it suitable for self-study or as a resource for upper-level coursework. Each chapter is self-contained and complemented by a comprehensive bibliography, ensuring its value as a long-lasting reference. An essential resource for theoretical and applied research, this book significantly contributes to the field of stochastic processes and will remain a key reference for years to come.
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Coupling and Ergodic Theorems for Semi-Markov-Type Processes II

Coupling and Ergodic Theorems for Semi-Markov-Type Processes II

Dmitrii Silvestrov

Springer International Publishing AG
2025
sidottu
Ergodic theorems are a cornerstone of the theory of stochastic processes and their applications. This book is the second volume of a two-volume monograph dedicated to ergodic theorems. While the first volume centers on Markovian and regenerative models, the second volume extends the scope to semi-Markov processes and multi-alternating regenerative processes with semi-Markov modulation and delves into ergodic theorems with explicit power and exponential upper bounds for convergence rates for such processes. The book offers a powerful and constructive probabilistic framework by employing coupling ergodic theorems presented in the first volume in conjunction with the method of artificial regeneration and test functions. Theoretical findings are illustrated with applications to semi-Markov Monte Carlo algorithms and perturbed queuing systems featuring explicit convergence rate bounds. Many results presented in the book are groundbreaking, appearing in publication for the first time. Designed with researchers and advanced students in mind, the content is thoughtfully structured by complexity, making it suitable for self-study or as a resource for upper-level coursework. Each chapter is self-contained and complemented by a comprehensive bibliography, ensuring its value as a long-lasting reference. An essential resource for theoretical and applied research, this book significantly contributes to the field of stochastic processes and will remain a key reference for years to come.
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American-Type Options

American-Type Options

Dmitrii S. Silvestrov

De Gruyter
2013
sidottu
The book gives a systematical presentation of stochastic approximation methods for models of American-type options with general pay-off functions for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The book also contains an extended bibliography of works in the area. This book is the first volume of the comprehensive two volumes monograph. The second volume will present results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.
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American-Type Options

American-Type Options

Dmitrii S. Silvestrov

De Gruyter
2014
sidottu
The book gives a systematical presentation of stochastic approximation methods for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The volume presents results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.
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Optimization of Stochastic Discrete Systems and Control on Complex Networks

Optimization of Stochastic Discrete Systems and Control on Complex Networks

Dmitrii Lozovanu; Stefan Pickl

Springer International Publishing AG
2014
sidottu
This book presents the latest findings on stochastic dynamic programming models and on solving optimal control problems in networks. It includes the authors’ new findings on determining the optimal solution of discrete optimal control problems in networks and on solving game variants of Markov decision problems in the context of computational networks. First, the book studies the finite state space of Markov processes and reviews the existing methods and algorithms for determining the main characteristics in Markov chains, before proposing new approaches based on dynamic programming and combinatorial methods. Chapter two is dedicated to infinite horizon stochastic discrete optimal control models and Markov decision problems with average and expected total discounted optimization criteria, while Chapter three develops a special game-theoretical approach to Markov decision processes and stochastic discrete optimal control problems. In closing, the book’s final chapter is devoted to finite horizon stochastic control problems and Markov decision processes. The algorithms developed represent a valuable contribution to the important field of computational network theory.
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Optimization of Stochastic Discrete Systems and Control on Complex Networks

Optimization of Stochastic Discrete Systems and Control on Complex Networks

Dmitrii Lozovanu; Stefan Pickl

Springer International Publishing AG
2016
nidottu
This book presents the latest findings on stochastic dynamic programming models and on solving optimal control problems in networks. It includes the authors’ new findings on determining the optimal solution of discrete optimal control problems in networks and on solving game variants of Markov decision problems in the context of computational networks. First, the book studies the finite state space of Markov processes and reviews the existing methods and algorithms for determining the main characteristics in Markov chains, before proposing new approaches based on dynamic programming and combinatorial methods. Chapter two is dedicated to infinite horizon stochastic discrete optimal control models and Markov decision problems with average and expected total discounted optimization criteria, while Chapter three develops a special game-theoretical approach to Markov decision processes and stochastic discrete optimal control problems. In closing, the book’s final chapter is devoted to finite horizon stochastic control problems and Markov decision processes. The algorithms developed represent a valuable contribution to the important field of computational network theory.
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Nonlinearly Perturbed Semi-Markov Processes

Nonlinearly Perturbed Semi-Markov Processes

Dmitrii Silvestrov; Sergei Silvestrov

Springer International Publishing AG
2017
nidottu
The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchersin the field of stochastic processes and their applications that will contribute to continuing extensive studies in the area and remain relevant for years to come.
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Optimization and Multiobjective Control of Time-Discrete Systems

Optimization and Multiobjective Control of Time-Discrete Systems

Dmitrii Lozovanu

Springer-Verlag Berlin and Heidelberg GmbH Co. K
2009
sidottu
Richard Bellmann developed a theory of dynamic programming which is for many reasons still in the center of great interest. The authors present a new approach in the ?eld of the optimization and multi-objective control of time-discrete systems which is closely related to the work of Richard Bellmann. They develop their own concept and their extension to the optimization and multi-objective control of time-discrete systems as well as to dynamic networks and multilayered structures are very stimulating for further research. Di?erent perspectives of discrete control and optimal dynamic ?ow problems on networks are treated and characterized. Together with the algorithmic solutions a framework of multi-objective control problems is - rived. The conclusion with a real world example underlines the necessity and - portance of their theoretic framework. As they come back to the classical Bellmann concept of dynamic programming they stress and honor his basic concept without debase their own work. Multilayereddecisionprocessesaspartofthedesignandanalysisofcomplexsystems and networks will be essential in many ways and ?elds in the future.
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Optimization and Multiobjective Control of Time-Discrete Systems

Optimization and Multiobjective Control of Time-Discrete Systems

Dmitrii Lozovanu

Springer-Verlag Berlin and Heidelberg GmbH Co. K
2010
nidottu
Richard Bellmann developed a theory of dynamic programming which is for many reasons still in the center of great interest. The authors present a new approach in the ?eld of the optimization and multi-objective control of time-discrete systems which is closely related to the work of Richard Bellmann. They develop their own concept and their extension to the optimization and multi-objective control of time-discrete systems as well as to dynamic networks and multilayered structures are very stimulating for further research. Di?erent perspectives of discrete control and optimal dynamic ?ow problems on networks are treated and characterized. Together with the algorithmic solutions a framework of multi-objective control problems is - rived. The conclusion with a real world example underlines the necessity and - portance of their theoretic framework. As they come back to the classical Bellmann concept of dynamic programming they stress and honor his basic concept without debase their own work. Multilayereddecisionprocessesaspartofthedesignandanalysisofcomplexsystems and networks will be essential in many ways and ?elds in the future.
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Metro 2035

Metro 2035

Dmitrii Glukhovskii

AST, Izdatel'stvo
2018
sidottu
Tretja mirovaja sterla chelovechestvo s litsa Zemli. Planeta opustela. Megapolisy obrascheny v prakh i pepel. Zheleznye dorogi rzhavejut. Sputniki odinoko boltajutsja na orbite. Radio molchit na vsekh chastotakh. Vyzhili tolko te, kto, uslyshav sireny trevogi, uspel dobezhat do dverej moskovskogo metro. Tam, na glubine v desjatki metrov, na stantsijakh i v tunneljakh, ljudi pytajutsja perezhdat konets sveta. Tam oni sozdali sebe novyj mirok vmesto poterjannogo ogromnogo mira. Oni tsepljajutsja za zhizn izo vsekh sil i otkazyvajutsja sdavatsja. Oni mechtajut vernutsja naverkh - odnazhdy, kogda radiatsionnyj fon ot jadernykh bombardirovok spadet. I ne ostavljajut nadezhdy najti drugikh vyzhivshikh… "Metro 2035" prodolzhaet - i zavershaet istoriju Artema iz pervoj knigi kultovoj trilogii. Etu knigu milliony chitatelej zhdali dolgie desjat let, i prava na perevod inostrannye izdateli vykupili zadolgo do togo, kak roman byl okonchen. Pri etom "2035" - kniga nezavisimaja, i imenno s nee mozhno nachat posvjaschenie v sagu, kotoraja pokorila Rossiju i ves mir.
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Metro 2033

Metro 2033

Dmitrii Glukhovskii

AST, Izdatel'stvo
2020
sidottu
The Third World War erased humanity from the face of the Earth. The planet is empty. Megalopolises are reduced to dust and ashes. The railways are rusting. Satellites wander lonely in orbit. The radio is silent on all frequencies. Only those survived who, having heard the alarm sirens, managed to run to the doors of the Moscow metro. There, at a depth of tens of meters, at stations and in tunnels, people are trying to wait out the end of the world. There they created a new world for themselves instead of the huge lost world. They cling to life with all their might and refuse to give up. They dream of returning to the top - one day, when the radiation background from nuclear bombings subsides. And they do not give up hope of finding other survivors ...The book is in Russian.
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Tekst

Tekst

Dmitrii Glukhovskii

AST, Izdatel'stvo
2019
sidottu
Studentu filfaka MGU Ile Gorjunovu molodoj politsejskij operativnik podbrasyvaet narkotiki, chtoby nakazat za stroptivost. Otbyv semiletnij srok, Ilja khochet prosto vernutsja k normalnoj zhizni — no vmesto etogo primerjaet na sebja zhizn cheloveka, kotoryj iskalechil emu sudbu..."Tekst" — eto roman o segodnjashnej Moskve, o segodnjashnej Rossii, o kazhdom iz nas. O nashem bespravii pered "organami", o nashej zavisimosti ot mobilnykh, o mesti i o proschenii, o nevozmozhnoj ljubvi i nesbytochnykh mechtakh. Nastojaschij novyj russkij roman, kotorogo ne pojavljalos tak davno.Vsego cherez dva goda posle vykhoda v svet "Tekst" uzhe pereveden bolee chem na 20 jazykov mira, frantsuzskaja i nemetskaja pressa sravnivajut roman s "Prestupleniem i nakazaniem", v Moskovskom teatre Ermolovoj po nemu postavlen iduschij s anshlagami spektakl i nedavno snjat film s glavnymi molodymi zvezdami rossijskogo kino. (2-e izdanie)
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Post

Post

Dmitrii Glukhovskii

AST, Izdatel'stvo
2021
sidottu
Novaja kniga Dmitrija Glukhovskogo, avtora kultovykh romanov "Metro 2033", "Tekst" i stsenarista telekhita "Topi"Obe chasti proekta "Post" pod odnoj oblozhkoj!Posle korotkoj i jarostnoj Grazhdanskoj vojny ot prezhnej Rossii ostalas lish nebolshaja chast, kotoraja nazyvaet sebja Moskovskoj imperiej. Vostochnye granitsy ee prokhodjat vsego v neskolkikh sotnjakh kilometrov ot stolitsy, po Volge - otravlennoj, prevrativshejsja v nepreodolimuju pregradu. S samogo Raspada nikto ne prikhodil v Moskoviju iz-za Volgi. Sama tysjacheletnjaja Moskva stoit nezyblemo, nadezhno zaschischennaja so vsekh storon okhrannymi postami. Tut provodit smotr kazachikh vojsk sam imperator. Luchshikh iz luchshikh, khrabrejshikh iz khrabrykh on vyberet, chtoby poslat ikh v temnye zemli, kotorye kogda-to byli chastju velikoj Rossii, - poka ikh ne okhvatil mjatezh i oni ne byli predany anafeme."Opredelenno luchshee iz napisannogo Dmitriem Glukhovskim na segodnja"Galina Juzefovich"Glukhovskij napisal dejstvitelno glubokij roman, vlozhiv v nego i filosofskie razmyshlenija, i khristianskij simvolizm, i osmyslenie segodnjashnej istorii, i jazykovuju stilizatsiju"Forbes"
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