Numerical Methods For Simulation And Optimization Of Piecewise Deterministic Markov Processes

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Numerical Methods for Simulation and Optimization of Piecewise Deterministic Markov Processes

Benoîte de Saporta,François Dufour,Huilong Zhang
Numerical Methods for Simulation and Optimization of Piecewise Deterministic Markov Processes Book PDF

Author : Benoîte de Saporta,François Dufour,Huilong Zhang
Publisher : John Wiley & Sons
Page : 298 pages
File Size : 41,7 Mb
Release : 2016-01-26
Category : Mathematics
ISBN : 9781848218390

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Numerical Methods for Simulation and Optimization of Piecewise Deterministic Markov Processes by Benoîte de Saporta,François Dufour,Huilong Zhang Pdf

Mark H.A. Davis introduced the Piecewise-Deterministic Markov Process (PDMP) class of stochastic hybrid models in an article in 1984. Today it is used to model a variety of complex systems in the fields of engineering, economics, management sciences, biology, Internet traffic, networks and many more. Yet, despite this, there is very little in the way of literature devoted to the development of numerical methods for PDMDs to solve problems of practical importance, or the computational control of PDMPs. This book therefore presents a collection of mathematical tools that have been recently developed to tackle such problems. It begins by doing so through examples in several application domains such as reliability. The second part is devoted to the study and simulation of expectations of functionals of PDMPs. Finally, the third part introduces the development of numerical techniques for optimal control problems such as stopping and impulse control problems.

Statistical Inference for Piecewise-deterministic Markov Processes

Romain Azais,Florian Bouguet
Statistical Inference for Piecewise deterministic Markov Processes Book PDF

Author : Romain Azais,Florian Bouguet
Publisher : John Wiley & Sons
Page : 300 pages
File Size : 42,7 Mb
Release : 2018-08-14
Category : Mathematics
ISBN : 9781786303028

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Statistical Inference for Piecewise-deterministic Markov Processes by Romain Azais,Florian Bouguet Pdf

Piecewise-deterministic Markov processes form a class of stochastic models with a sizeable scope of applications: biology, insurance, neuroscience, networks, finance... Such processes are defined by a deterministic motion punctuated by random jumps at random times, and offer simple yet challenging models to study. Nevertheless, the issue of statistical estimation of the parameters ruling the jump mechanism is far from trivial. Responding to new developments in the field as well as to current research interests and needs, Statistical inference for piecewise-deterministic Markov processes offers a detailed and comprehensive survey of state-of-the-art results. It covers a wide range of general processes as well as applied models. The present book also dwells on statistics in the context of Markov chains, since piecewise-deterministic Markov processes are characterized by an embedded Markov chain corresponding to the position of the process right after the jumps.

Markov Renewal and Piecewise Deterministic Processes

Christiane Cocozza-Thivent
Markov Renewal and Piecewise Deterministic Processes Book PDF

Author : Christiane Cocozza-Thivent
Publisher : Springer Nature
Page : 252 pages
File Size : 54,7 Mb
Release : 2021-06-09
Category : Mathematics
ISBN : 9783030704476

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Markov Renewal and Piecewise Deterministic Processes by Christiane Cocozza-Thivent Pdf

This book is aimed at researchers, graduate students and engineers who would like to be initiated to Piecewise Deterministic Markov Processes (PDMPs). A PDMP models a deterministic mechanism modified by jumps that occur at random times. The fields of applications are numerous : insurance and risk, biology, communication networks, dependability, supply management, etc. Indeed, the PDMPs studied so far are in fact deterministic functions of CSMPs (Completed Semi-Markov Processes), i.e. semi-Markov processes completed to become Markov processes. This remark leads to considerably broaden the definition of PDMPs and allows their properties to be deduced from those of CSMPs, which are easier to grasp. Stability is studied within a very general framework. In the other chapters, the results become more accurate as the assumptions become more precise. Generalized Chapman-Kolmogorov equations lead to numerical schemes. The last chapter is an opening on processes for which the deterministic flow of the PDMP is replaced with a Markov process. Marked point processes play a key role throughout this book.

Mathematical Modeling of Random and Deterministic Phenomena

Solym Mawaki Manou-Abi,Sophie Dabo-Niang,Jean-Jacques Salone
Mathematical Modeling of Random and Deterministic Phenomena Book PDF

Author : Solym Mawaki Manou-Abi,Sophie Dabo-Niang,Jean-Jacques Salone
Publisher : John Wiley & Sons
Page : 350 pages
File Size : 46,7 Mb
Release : 2020-02-25
Category : Juvenile Nonfiction
ISBN : 9781119706908

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Mathematical Modeling of Random and Deterministic Phenomena by Solym Mawaki Manou-Abi,Sophie Dabo-Niang,Jean-Jacques Salone Pdf

This book highlights mathematical research interests that appear in real life, such as the study and modeling of random and deterministic phenomena. As such, it provides current research in mathematics, with applications in biological and environmental sciences, ecology, epidemiology and social perspectives. The chapters can be read independently of each other, with dedicated references specific to each chapter. The book is organized in two main parts. The first is devoted to some advanced mathematical problems regarding epidemic models; predictions of biomass; space-time modeling of extreme rainfall; modeling with the piecewise deterministic Markov process; optimal control problems; evolution equations in a periodic environment; and the analysis of the heat equation. The second is devoted to a modelization with interdisciplinarity in ecological, socio-economic, epistemological, demographic and social problems. Mathematical Modeling of Random and Deterministic Phenomena is aimed at expert readers, young researchers, plus graduate and advanced undergraduate students who are interested in probability, statistics, modeling and mathematical analysis.

Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences

Maksym Luz,Mikhail Moklyachuk
Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences Book PDF

Author : Maksym Luz,Mikhail Moklyachuk
Publisher : John Wiley & Sons
Page : 293 pages
File Size : 46,6 Mb
Release : 2019-09-25
Category : Mathematics
ISBN : 9781119663508

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Estimation of Stochastic Processes with Stationary Increments and Cointegrated Sequences by Maksym Luz,Mikhail Moklyachuk Pdf

Estimation of Stochastic Processes is intended for researchers in the field of econometrics, financial mathematics, statistics or signal processing. This book gives a deep understanding of spectral theory and estimation techniques for stochastic processes with stationary increments. It focuses on the estimation of functionals of unobserved values for stochastic processes with stationary increments, including ARIMA processes, seasonal time series and a class of cointegrated sequences. Furthermore, this book presents solutions to extrapolation (forecast), interpolation (missed values estimation) and filtering (smoothing) problems based on observations with and without noise, in discrete and continuous time domains. Extending the classical approach applied when the spectral densities of the processes are known, the minimax method of estimation is developed for a case where the spectral information is incomplete and the relations that determine the least favorable spectral densities for the optimal estimations are found.

Theory and Statistical Applications of Stochastic Processes

Yuliya Mishura,Georgiy Shevchenko
Theory and Statistical Applications of Stochastic Processes Book PDF

Author : Yuliya Mishura,Georgiy Shevchenko
Publisher : John Wiley & Sons
Page : 400 pages
File Size : 44,5 Mb
Release : 2018-01-04
Category : Mathematics
ISBN : 9781786300508

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Theory and Statistical Applications of Stochastic Processes by Yuliya Mishura,Georgiy Shevchenko Pdf

This book is concerned with the theory of stochastic processes and the theoretical aspects of statistics for stochastic processes. It combines classic topics such as construction of stochastic processes, associated filtrations, processes with independent increments, Gaussian processes, martingales, Markov properties, continuity and related properties of trajectories with contemporary subjects: integration with respect to Gaussian processes, Itȏ integration, stochastic analysis, stochastic differential equations, fractional Brownian motion and parameter estimation in diffusion models.

Random Motions in Markov and Semi-Markov Random Environments 1

Anatoliy Pogorui,Anatoliy Swishchuk,Ramon M. Rodriguez-Dagnino
Random Motions in Markov and Semi Markov Random Environments 1 Book PDF

Author : Anatoliy Pogorui,Anatoliy Swishchuk,Ramon M. Rodriguez-Dagnino
Publisher : John Wiley & Sons
Page : 256 pages
File Size : 48,7 Mb
Release : 2021-01-12
Category : Mathematics
ISBN : 9781119808183

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Random Motions in Markov and Semi-Markov Random Environments 1 by Anatoliy Pogorui,Anatoliy Swishchuk,Ramon M. Rodriguez-Dagnino Pdf

This book is the first of two volumes on random motions in Markov and semi-Markov random environments. This first volume focuses on homogenous random motions. This volume consists of two parts, the first describing the basic concepts and methods that have been developed for random evolutions. These methods are the foundational tools used in both volumes, and this description includes many results in potential operators. Some techniques to find closed-form expressions in relevant applications are also presented. The second part deals with asymptotic results and presents a variety of applications, including random motion with different types of boundaries, the reliability of storage systems and solutions of partial differential equations with constant coefficients, using commutative algebra techniques. It also presents an alternative formulation to the Black-Scholes formula in finance, fading evolutions and telegraph processes, including jump telegraph processes and the estimation of the number of level crossings for telegraph processes.

Random Motions in Markov and Semi-Markov Random Environments 2

Anatoliy Pogorui,Anatoliy Swishchuk,Ramon M. Rodriguez-Dagnino
Random Motions in Markov and Semi Markov Random Environments 2 Book PDF

Author : Anatoliy Pogorui,Anatoliy Swishchuk,Ramon M. Rodriguez-Dagnino
Publisher : John Wiley & Sons
Page : 224 pages
File Size : 48,8 Mb
Release : 2021-01-11
Category : Mathematics
ISBN : 9781119808176

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Random Motions in Markov and Semi-Markov Random Environments 2 by Anatoliy Pogorui,Anatoliy Swishchuk,Ramon M. Rodriguez-Dagnino Pdf

This book is the second of two volumes on random motions in Markov and semi-Markov random environments. This second volume focuses on high-dimensional random motions. This volume consists of two parts. The first expands many of the results found in Volume 1 to higher dimensions. It presents new results on the random motion of the realistic three-dimensional case, which has so far been barely mentioned in the literature, and deals with the interaction of particles in Markov and semi-Markov media, which has, in contrast, been a topic of intense study. The second part contains applications of Markov and semi-Markov motions in mathematical finance. It includes applications of telegraph processes in modeling stock price dynamics and investigates the pricing of variance, volatility, covariance and correlation swaps with Markov volatility and the same pricing swaps with semi-Markov volatilities.

Asymptotic Analyses for Complex Evolutionary Systems with Markov and Semi-Markov Switching Using Approximation Schemes

Yaroslav Chabanyuk,Anatolii Nikitin,Uliana Khimka
Asymptotic Analyses for Complex Evolutionary Systems with Markov and Semi Markov Switching Using Approximation Schemes Book PDF

Author : Yaroslav Chabanyuk,Anatolii Nikitin,Uliana Khimka
Publisher : John Wiley & Sons
Page : 240 pages
File Size : 53,6 Mb
Release : 2020-11-02
Category : Mathematics
ISBN : 9781119779735

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Asymptotic Analyses for Complex Evolutionary Systems with Markov and Semi-Markov Switching Using Approximation Schemes by Yaroslav Chabanyuk,Anatolii Nikitin,Uliana Khimka Pdf

This book analyzes stochastic evolutionary models under the impulse of diffusion, as well as Markov and semi-Markov switches. Models are investigated under the conditions of classical and non-classical (Levy and Poisson) approximations in addition to jumping stochastic approximations and continuous optimization procedures. Among other asymptotic properties, particular attention is given to weak convergence, dissipativity, stability and the control of processes and their generators. Weak convergence of stochastic processes is usually proved by verifying two conditions: the tightness of the distributions of the converging processes, which ensures the existence of a converging subsequence, and the uniqueness of the weak limit. Achieving the limit can be done on the semigroups that correspond to the converging process as well as on appropriate generators. While this provides the convergence of generators, a natural question arises concerning the uniqueness of a limit semigroup.

Semi-Markov Migration Models for Credit Risk

Guglielmo D'Amico,Giuseppe Di Biase,Jacques Janssen,Raimondo Manca
Semi Markov Migration Models for Credit Risk Book PDF

Author : Guglielmo D'Amico,Giuseppe Di Biase,Jacques Janssen,Raimondo Manca
Publisher : John Wiley & Sons
Page : 318 pages
File Size : 44,5 Mb
Release : 2017-06-26
Category : Mathematics
ISBN : 9781848219052

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Semi-Markov Migration Models for Credit Risk by Guglielmo D'Amico,Giuseppe Di Biase,Jacques Janssen,Raimondo Manca Pdf

Credit risk is one of the most important contemporary problems for banks and insurance companies. Indeed, for banks, more than forty percent of the equities are necessary to cover this risk. Though this problem is studied by large rating agencies with substantial economic, social and financial tools, building stochastic models is nevertheless necessary to complete this descriptive orientation. This book presents a complete presentation of such a category of models using homogeneous and non-homogeneous semi-Markov processes developed by the authors in several recent papers. This approach provides a good method of evaluating the default risk and the classical VaR indicators used for Solvency II and Basel III governance rules. This book is the first to present a complete semi-Markov treatment of credit risk while also insisting on the practical use of the models presented here, including numerical aspects, so that this book is not only useful for scientific research but also to managers working in this field for banks, insurance companies, pension funds and other financial institutions.

Earthquake Statistical Analysis through Multi-state Modeling

Irene Votsi,Nikolaos Limnios,Eleftheria Papadimitriou,George Tsaklidis
Earthquake Statistical Analysis through Multi state Modeling Book PDF

Author : Irene Votsi,Nikolaos Limnios,Eleftheria Papadimitriou,George Tsaklidis
Publisher : John Wiley & Sons
Page : 196 pages
File Size : 50,8 Mb
Release : 2019-04-02
Category : Mathematics
ISBN : 9781786301505

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Earthquake Statistical Analysis through Multi-state Modeling by Irene Votsi,Nikolaos Limnios,Eleftheria Papadimitriou,George Tsaklidis Pdf

Earthquake occurrence modeling is a rapidly developing research area. This book deals with its critical issues, ranging from theoretical advances to practical applications. The introductory chapter outlines state-of-the-art earthquake modeling approaches based on stochastic models. Chapter 2 presents seismogenesis in association with the evolving stress field. Chapters 3 to 5 present earthquake occurrence modeling by means of hidden (semi-)Markov models and discuss associated characteristic measures and relative estimation aspects. Further comparisons, the most important results and our concluding remarks are provided in Chapters 6 and 7.

Introduction to Matrix-Analytic Methods in Queues 2

Srinivas R. Chakravarthy
Introduction to Matrix Analytic Methods in Queues 2 Book PDF

Author : Srinivas R. Chakravarthy
Publisher : John Wiley & Sons
Page : 453 pages
File Size : 48,5 Mb
Release : 2022-10-18
Category : Mathematics
ISBN : 9781786308238

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Introduction to Matrix-Analytic Methods in Queues 2 by Srinivas R. Chakravarthy Pdf

Matrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since. In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and explains the results using a number of worked-out examples. This book's approach will inform and kindle the interest of researchers attracted to this fertile field. To allow readers to practice and gain experience in the algorithmic and computational procedures of MAM, Introduction to Matrix-Analytic Methods in Queues 2 provides a number of computational exercises. It also incorporates simulation as another tool for studying complex stochastic models, especially when the state space of the underlying stochastic models under analytic study grows exponentially. This book's detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.

Controlled Branching Processes

Miguel González Velasco,Inés María Del Puerto García,George Petrov Yanev
Controlled Branching Processes Book PDF

Author : Miguel González Velasco,Inés María Del Puerto García,George Petrov Yanev
Publisher : John Wiley & Sons
Page : 232 pages
File Size : 43,7 Mb
Release : 2017-12-27
Category : Mathematics
ISBN : 9781119484646

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Controlled Branching Processes by Miguel González Velasco,Inés María Del Puerto García,George Petrov Yanev Pdf

The purpose of this book is to provide a comprehensive discussion of the available results for discrete time branching processes with random control functions. The independence of individuals’ reproduction is a fundamental assumption in the classical branching processes. Alternatively, the controlled branching processes (CBPs) allow the number of reproductive individuals in one generation to decrease or increase depending on the size of the previous generation. Generating a wide range of behaviors, the CBPs have been successfully used as modeling tools in diverse areas of applications.

Traditional Functional-Discrete Methods for the Problems of Mathematical Physics

Volodymyr Makarov,Nataliya Mayko
Traditional Functional Discrete Methods for the Problems of Mathematical Physics Book PDF

Author : Volodymyr Makarov,Nataliya Mayko
Publisher : John Wiley & Sons
Page : 282 pages
File Size : 44,5 Mb
Release : 2024-02-23
Category : Science
ISBN : 9781394276653

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Traditional Functional-Discrete Methods for the Problems of Mathematical Physics by Volodymyr Makarov,Nataliya Mayko Pdf

This book is devoted to the construction and study of approximate methods for solving mathematical physics problems in canonical domains. It focuses on obtaining weighted a priori estimates of the accuracy of these methods while also considering the influence of boundary and initial conditions. This influence is quantified by means of suitable weight functions that characterize the distance of an inner point to the boundary of the domain. New results are presented on boundary and initial effects for the finite difference method for elliptic and parabolic equations, mesh schemes for equations with fractional derivatives, and the Cayley transform method for abstract differential equations in Hilbert and Banach spaces. Due to their universality and convenient implementation, the algorithms discussed throughout can be used to solve a wide range of actual problems in science and technology. The book is intended for scientists, university teachers, and graduate and postgraduate students who specialize in the field of numerical analysis.

Statistical Topics and Stochastic Models for Dependent Data with Applications

Vlad Stefan Barbu,Nicolas Vergne
Statistical Topics and Stochastic Models for Dependent Data with Applications Book PDF

Author : Vlad Stefan Barbu,Nicolas Vergne
Publisher : John Wiley & Sons
Page : 288 pages
File Size : 45,8 Mb
Release : 2020-10-09
Category : Mathematics
ISBN : 9781119779414

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Statistical Topics and Stochastic Models for Dependent Data with Applications by Vlad Stefan Barbu,Nicolas Vergne Pdf

This book is a collective volume authored by leading scientists in the field of stochastic modelling, associated statistical topics and corresponding applications. The main classes of stochastic processes for dependent data investigated throughout this book are Markov, semi-Markov, autoregressive and piecewise deterministic Markov models. The material is divided into three parts corresponding to: (i) Markov and semi-Markov processes, (ii) autoregressive processes and (iii) techniques based on divergence measures and entropies. A special attention is payed to applications in reliability, survival analysis and related fields.