Stochastic Equations

Stochastic Optimal Control in Infinite Dimension: Dynamic Programming and HJB Equations

Giorgio Fabbri, "Stochastic Optimal Control in Infinite Dimension: Dynamic Programming and HJB Equations"
English | ISBN: 3319530666 | 2017 | 910 pages | PDF | 11 MB

Numerical Solution of Stochastic Differential Equations  eBooks & eLearning

Posted by AvaxGenius at Dec. 10, 2020
Numerical Solution of Stochastic Differential Equations

Numerical Solution of Stochastic Differential Equations by Peter E. Kloeden
English | PDF | 1992 | 666 Pages | ISBN : 364208107X | 48.2 MB

The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, in both theory and applications, emphasising the numerical methods needed to solve such equations. It assumes of the reader an undergraduate background in mathematical methods typical of engineers and physicists, though many chapters begin with a descriptive summary.

Stochastic Differential Equations: An Introduction with Applications, Third Edition  eBooks & eLearning

Posted by AvaxGenius at Jan. 2, 2024
Stochastic Differential Equations: An Introduction with Applications, Third Edition

Stochastic Differential Equations: An Introduction with Applications, Third Edition by Bernt Øksendal
English | PDF | 1992 | 240 Pages | ISBN : 3540533354 | 12 MB

From the reviews to the first edition: Most of the literature about stochastic differential equations seems to place so much emphasis on rigor and completeness that it scares the nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view.: Not knowing anything … about a subject to start with, what would I like to know first of all. My answer would be: 1) In what situations does the subject arise ? 2) What are its essential features? 3) What are the applications and the connections to other fields?" The author, a lucid mind with a fine pedagocical instinct, has written a splendid text that achieves his aims set forward above. He starts out by stating six problems in the introduction in which stochastic differential equations play an essential role in the solution. Then, while developing stochastic calculus, he frequently returns to these problems and variants thereof and to many other problems to show how thetheory works and to motivate the next step in the theoretical development. Needless to say, he restricts himself to stochastic integration with respectto Brownian motion. He is not hesitant to give some basic results without proof in order to leave room for "some more basic applications"… It can be an ideal text for a graduate course, but it is also recommended to analysts (in particular, those working in differential equations and deterministic dynamical systems and control) who wish to learn quickly what stochastic differential equations are all about. From: Acta Scientiarum Mathematicarum, Tom 50, 3-4, 1986.
Numerical Approximations of Stochastic Maxwell Equations: via Structure-Preserving Algorithms

Numerical Approximations of Stochastic Maxwell Equations: via Structure-Preserving Algorithms by Chuchu Chen , Jialin Hong , Lihai Ji
English | PDF EPUB (True) | 2024 | 293 Pages | ISBN : 981996685X | 40.8 MB

The stochastic Maxwell equations play an essential role in many fields, including fluctuational electrodynamics, statistical radiophysics, integrated circuits, and stochastic inverse problems.

Fractional Stochastic Differential Equations: Applications to Covid-19 Modeling  eBooks & eLearning

Posted by AvaxGenius at April 25, 2022
Fractional Stochastic Differential Equations: Applications to Covid-19 Modeling

Fractional Stochastic Differential Equations: Applications to Covid-19 Modeling by Abdon Atangana
English | PDF,EPUB | 2022 | 552 Pages | ISBN : 9811907285 | 128 MB

This book provides a thorough conversation on the underpinnings of Covid-19 spread modelling by using stochastics nonlocal differential and integral operators with singular and non-singular kernels.

Numerical Solution of Stochastic Differential Equations with Jumps in Finance (Repost)  eBooks & eLearning

Posted by AvaxGenius at Dec. 10, 2020
Numerical Solution of Stochastic Differential Equations with Jumps in Finance (Repost)

Numerical Solution of Stochastic Differential Equations with Jumps in Finance by Eckhard Platen
English | PDF | 2010 | 868 Pages | ISBN : 3642120571 | 18 MB

In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992).

Modeling with Itô Stochastic Differential Equations (Repost)  eBooks & eLearning

Posted by AvaxGenius at March 2, 2024
Modeling with Itô Stochastic Differential Equations (Repost)

Modeling with Itô Stochastic Differential Equations by E. Allen
English | PDF | 2007 | 238 Pages | ISBN : 1402059523 | 1.6 MB

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 system is obtained.
General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions (Repost

General Pontryagin-Type Stochastic Maximum Principle and Backward Stochastic Evolution Equations in Infinite Dimensions by Qi Lü, Xu Zhang
English | PDF | 2014 | 148 Pages | ISBN : 3319066315 | 1.7 MB

The classical Pontryagin maximum principle (addressed to deterministic finite dimensional control systems) is one of the three milestones in modern control theory. The corresponding theory is by now well-developed in the deterministic infinite dimensional setting and for the stochastic differential equations. However, very little is known about the same problem but for controlled stochastic (infinite dimensional) evolution equations when the diffusion term contains the control variables and the control domains are allowed to be non-convex. Indeed, it is one of the longstanding unsolved problems in stochastic control theory to establish the Pontryagintype maximum principle for this kind of general control systems: this book aims to give a solution to this problem. This book will be useful for both beginners and experts who are interested in optimal control theory for stochastic evolution equations.

Taylor Approximations for Stochastic Partial Differential Equations  eBooks & eLearning

Posted by arundhati at May 19, 2020
Taylor Approximations for Stochastic Partial Differential Equations

Arnulf Jentzen, "Taylor Approximations for Stochastic Partial Differential Equations "
English | ISBN: 1611972000 | 2011 | 235 pages | PDF | 1424 KB

Probability and Partial Differential Equations in Modern Applied Mathematics  eBooks & eLearning

Posted by AvaxGenius at Jan. 27, 2023
Probability and Partial Differential Equations in Modern Applied Mathematics

Probability and Partial Differential Equations in Modern Applied Mathematics by Edward C. Waymire, Jinqiao Duan
English | PDF(True) | 2005 | 265 Pages | ISBN : 0387258795 | 22 MB

"Probability and Partial Differential Equations in Modern Applied Mathematics" is devoted to the role of probabilistic methods in modern applied mathematics from the perspectives of both a tool for analysis and as a tool in modeling. There is a recognition in the applied mathematics research community that stochastic methods are playing an increasingly prominent role in the formulation and analysis of diverse problems of contemporary interest in the sciences and engineering. A probabilistic representation of solutions to partial differential equations that arise as deterministic models allows one to exploit the power of stochastic calculus and probabilistic limit theory in the analysis of deterministic problems, as well as to offer new perspectives on the phenomena for modeling purposes.