Stochastic Processes

Random processes are one of the most powerful tools in the study and understanding of countless phenomena in natural and social sciences.The book is a complete medium-level introduction to the subject. The book is written in a clear and pedagogical...

The book provides the background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on...

The book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of...

Why should we use white noise analysis? Well, one reason of course is that it fills that earlier gap in the tool kit. As Hida would put it, white noise provides us with a useful set of independent coordinates, parametrized by 'time'. And there is a...

This volume is to pique the interest of many researchers in the fields of infinite dimensional analysis and quantum probability. These fields have undergone increasingly significant developments and have found many new applications, in particular, to...

This book concerns continuous-time controlled Markov chains, also known as continuous-time Markov decision processes. They form a class of stochastic control problems in which a single decision-maker wishes to optimize a given objective function. This...

Stochastic Differential Equations for Science and Engineering is aimed at students at the M.Sc. and PhD level. The book describes the mathematical construction of stochastic differential equations with a level of detail suitable to the audience, while...

Diffusion Processes, Jump Processes, and Stochastic Differential Equations provides a compact exposition of the results explaining interrelations between diffusion stochastic processes, stochastic differential equations and the fractional infinitesimal...

This book is devoted to the study of stochastic measures (SMs). An SM is a sigma-additive in probability random function, defined on a sigma-algebra of sets. SMs can be generated by the increments of random processes from many important classes such as...

The book presents, for the first time, a detailed analysis of harmonizable processes and fields (in the weak sense) that contain the corresponding stationary theory as a subclass. It also gives the structural and some key applications in detail. These...

This book aims to provide an overview of the special functions of fractional calculus and their applications in diffusion and random search processes. The book contains detailed calculations for various examples of anomalous diffusion, random search and...

Interacting particle systems are Markov processes involving infinitely many interacting components. Since their introduction in the 1970s, researchers have found many applications in statistical physics and population biology. Genealogies, which follow...

This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical...

The objective of this book is to introduce the elements of stochastic processes in a rather concise manner where we present the two most important parts - Markov chains and stochastic analysis. The readers are led directly to the core of the main topics...

This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This...

Praise for the First Edition ". . . an excellent textbook . . . well organized and neatly written." -Mathematical Reviews ". . . amazingly interesting . . ." -Technometrics Thoroughly updated to showcase the interrelationships between probability,...

'... the volume is impressively accessible. The result is a book that is valuable and approachable for biologists at all levels, including those interested in deepening their skills in mathematical modeling and those who seek an overview to aid them in...

Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory. New in this edition is an introduction to measure theory that expands the market, as this...

Interest rate modeling and the pricing of related derivatives remain subjects of increasing importance in financial mathematics and risk management. This book provides an accessible introduction to these topics by a step-by-step presentation of concepts...

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An expert integration of digital twin technology and advanced simulation methods for the design and optimization of electronic packaging systems In Stochastic Finite Element Modeling in Electronic Packaging, distinguished researcher Liu Chu delivers an...

In applications of stochastic calculus, there are phenomena that cannot be analyzed through the classical Ito theory. It is necessary, therefore, to have a theory based on stochastic integration with respect to these situations.Theory of Stochastic...

This is the first book that presents the theory of stochastic integral using the generalized Riemann approach. Readers who are familiar with undergraduate calculus and want to have an easy access to the theory of stochastic integral will find most of...

Corresponding to the link of Ito's stochastic differential equations (SDEs) and linear parabolic equations, distribution dependent SDEs (DDSDEs) characterize nonlinear Fokker-Planck equations. This type of SDEs is named after McKean-Vlasov due to the...

This text gives a comprehensive, largely self-contained treatment of multivariate heavy tail analysis. Emphasizing regular variation of measures means theory can be presented systematically and without regard to dimension. Tools are developed that allow...

This is the first comprehensive book on Trotter-Kato approximations of stochastic differential equations (SDEs) in infinite dimensions and applications. This research monograph brings together the varied literature on this topic since 1985 when such a...