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Stochastic Differential Equations
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B K Ksendal, Bernt Oksendal
This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without ...
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Numerical Solution of Stochastic Differential Equations
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Peter E Kloeden
The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic calculus. The book proposes to the reader whose background knowledge is limited to undergraduate level methods for engineering and physics, and easily accessible introductions to SDE ...
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Numerical Solution of Sde Through Computer Experiments
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Peter E Kloeden, Eckhard Platen, Henri Schurz
The book provides an easily accessible computationally oriented introduction into the numerical solution of stochastic differential equations using computer experiments. It develops in the reader an ability to apply numerical methods solving stochastic differential equations in their own fields. Furthermore, it creates an intuitive understanding ...
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Stochastic Dynamics
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Hans Crauel (Editor), Matthias Gundlach (Editor)
This volume gives an account of new and recent developments in the theory of random and, in particular, stochastic dynamical systems. Its purpose is to document and, to some extent, summarise the current state of the field of random dynamical systems beyond the recent monograph, "Random Dynamical Systems" by Ludwig Arnold. The book is intended for ...
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Exponential Stability of Stochastic Differential Equations
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Mao
This work presents a systematic study of current developments in stochastic differential delay equations driven by nonlinear integrators, detailing various exponential stabilities for stochastic differential equations and large-scale systems. It illustrates the practical use of stochastic stabilization, stochastic destabilization, stochastic flows ...
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Simulation and Inference for Stochastic Differential Equations: With R Examples
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Stefano M Iacus
This book is unique because of its focus on the practical implementation of the simulation and estimation methods presented. The book will be useful to practitioners and students with only a minimal mathematical background because of the many R programs, and to more mathematically-educated practitioners. Many of the methods presented in the book ...
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Stochastic Integration and Differential Equations
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Philip Protter
It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many other texts on the same subject have been published, often with connections to applications, especially mathematical finance. Yet in spite of the apparent simplicity of approach, none of these books ...
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Backward Stochastic Differential Equations
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Nicole El Karoui (Editor), Nicole Karoui, Laurent Mazliak (Editor)
This book presents the texts of seminars presented during the years 1995 and 1996 at the Universit? Paris VI and is the first attempt to present a survey on this subject. Starting from the classical conditions for existence and unicity of a solution in the most simple case-which requires more than basic stochartic calculus-several refinements on ...
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Noise-Induced Phenomena in Slow-Fast Dynamical Systems: A Sample-Paths Approach
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Nils Berglund, Barbara Gentz
Stochastic differential equations play an increasingly important role in modeling the dynamics of a large variety of systems in the natural sciences, and in technological applications. This book is aimed at advanced undergraduate and graduate students, and researchers in mathematics, physics, the natural sciences, and engineering. It presents a ...
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Singular Stochastic Differential Equations
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Alexander S Cherny, Hans-J]rgen Engelbert
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and ...
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Modeling with Ito Stochastic Differential Equations
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E Allen
Dynamical systems with random influences occur throughout the physical, biological, and social sciences. By carefully studying a randomly varying system over a small time interval, a discrete stochastic process model can be constructed. Next, letting the time interval shrink to zero, an Ito stochastic differential equation model for the dynamical ...
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Theory of Stochastic Differential Equations with Jumps and Applications: Mathematical and Analytical Techniques with Applications to Engineering
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by
Rong Situ
Stochastic differential equations (SDEs) are a powerful tool in science, mathematics, economics and finance. This book will help the reader to master the basic theory and learn some applications of SDEs. In particular, the reader will be provided with the backward SDE technique for use in research when considering financial problems in the market, ...
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Topological Dynamics of Random Dynamical Systems
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Nguyen Dinh Cong
This book is devoted to the theory of topological dynamics of random dynamical systems. The theory of random dynamical systems is a relatively new and fast expanding field of research which attracts the attention of researchers from various fields of science. It unites and develops the classical deterministic theory of dynamical systems and ...
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Forward-Backward Stochastic Differential Equations and Their Applications
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Jin Ma, Jiongmin Yong
This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the "Four Step Scheme", and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are ...
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Stochastic Space-Time Models and Limit Theorems
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P Kotelenez (Editor), L Arnold (Editor)
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Stochastic Differential Equations & Applications
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Avner Friedman
This text develops the theory of systems of stochastic differential equations and presents applications in probability, partial differential equations, and stochastic control problems. Originally published in 2 volumes, it combines a book of basic theory with a book of applications. Familiarity with elementary probability is the sole prerequisite. ...
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Stochastic Differential and Difference Equations
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Imre Csizar, Imre Csiszar, Gy Michaletzky
This volume contains a selection of papers presented at the Conference on Stochastic Differential and Difference Equations held in Hungary, August 1996. The papers cover a wide range of contemporary topics in stochastics with particular reference to control theory.
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Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces
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Kiyosi Ito, Kiyosi Ito
A systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite ...
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From Elementary Probability to Stochastic Differential Equations with Maple
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Peter E Kloeden, Sasha Cyganowski, Jerzy Ombach
The authors provide a fast introduction to probabilistic and statistical concepts necessary to understand the basic ideas and methods of stochastic differential equations. The book is based on measure theory which is introduced as smoothly as possible. It is intended for advanced undergraduate students or graduates, not necessarily in mathematics, ...
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Stochastic Differential Equations, with Applications to Physics and Engineering
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Kazimierz Sobczyk
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Stochastic Differential Equations: An Introduction with Applications
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by
B K Ksendal
This text gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications, for example, economics, biology and physics. The idea of the presentation is to start from some basic results (without ...
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Stochastic integration and differential equations a new approach
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by
Protter
This book is quite different from others on the subject in that it presents a rapid introduction to the modern semimartingale theory of stochastic integration and differential equations, without first having to treat the beautiful but highly technical "general theory of processes". The author's new approach (based on the theorem of Bitcheler ...
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Stability of Infinite Dimensional Stochastic Differential Equations with Applications
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Kai Liu, Haim Brezis, Alan Jeffrey
Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well ...
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Stochastic Flows and Stochastic Differential Equations
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Hiroshi Kunita
The main purpose of this book is to give a systematic treatment of the theory of stochastic differential equations and stochastic flow of diffeomorphisms, and through the former to study the properties of stochastic flows. The classical theory was initiated by K. Ito and since then has been much developed. Professor Kunita's approach here is to ...
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Stochastic Differential Equations
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Joseph Bishop Keller, Society for Industrial and Applied Mathe
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