Stochastic Flows and Jump-diffusions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Flows and Jump-diffusions write by H. Kunita. This book was released on 2019. Stochastic Flows and Jump-diffusions available in PDF, EPUB and Kindle. This monograph presents a modern treatment of (1) stochastic differential equations and (2) diffusion and jump-diffusion processes. The simultaneous treatment of diffusion processes and jump processes in this book is unique: Each chapter starts from continuous processes and then proceeds to processes with jumps. In the first part of the book, it is shown that solutions of stochastic differential equations define stochastic flows of diffeomorphisms. Then, the relation between stochastic flows and heat equations is discussed. The latter part investigates fundamental solutions of these heat equations (heat kernels) through the study of the Malliavin calculus. The author obtains smooth densities for transition functions of various types of diffusions and jump-diffusions and shows that these density functions are fundamental solutions for various types of heat equations and backward heat equations. Thus, in this book fundamental solutions for heat equations and backward heat equations are constructed independently of the theory of partial differential equations. Researchers and graduate student in probability theory will find this book very useful.
Stochastic Flows and Jump-Diffusions
Stochastic Flows and Jump-Diffusions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Flows and Jump-Diffusions write by Hiroshi Kunita. This book was released on 2019-03-26. Stochastic Flows and Jump-Diffusions available in PDF, EPUB and Kindle. This monograph presents a modern treatment of (1) stochastic differential equations and (2) diffusion and jump-diffusion processes. The simultaneous treatment of diffusion processes and jump processes in this book is unique: Each chapter starts from continuous processes and then proceeds to processes with jumps.In the first part of the book, it is shown that solutions of stochastic differential equations define stochastic flows of diffeomorphisms. Then, the relation between stochastic flows and heat equations is discussed. The latter part investigates fundamental solutions of these heat equations (heat kernels) through the study of the Malliavin calculus. The author obtains smooth densities for transition functions of various types of diffusions and jump-diffusions and shows that these density functions are fundamental solutions for various types of heat equations and backward heat equations. Thus, in this book fundamental solutions for heat equations and backward heat equations are constructed independently of the theory of partial differential equations.Researchers and graduate student in probability theory will find this book very useful.
Stochastic Flows and Jump-Diffusions
Stochastic Flows and Jump-Diffusions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Flows and Jump-Diffusions write by Hiroshi Kunita. This book was released on 2019-05-06. Stochastic Flows and Jump-Diffusions available in PDF, EPUB and Kindle. This monograph presents a modern treatment of (1) stochastic differential equations and (2) diffusion and jump-diffusion processes. The simultaneous treatment of diffusion processes and jump processes in this book is unique: Each chapter starts from continuous processes and then proceeds to processes with jumps.In the first part of the book, it is shown that solutions of stochastic differential equations define stochastic flows of diffeomorphisms. Then, the relation between stochastic flows and heat equations is discussed. The latter part investigates fundamental solutions of these heat equations (heat kernels) through the study of the Malliavin calculus. The author obtains smooth densities for transition functions of various types of diffusions and jump-diffusions and shows that these density functions are fundamental solutions for various types of heat equations and backward heat equations. Thus, in this book fundamental solutions for heat equations and backward heat equations are constructed independently of the theory of partial differential equations.Researchers and graduate student in probability theory will find this book very useful.
Applied Stochastic Control of Jump Diffusions
Applied Stochastic Control of Jump Diffusions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Applied Stochastic Control of Jump Diffusions write by Bernt Øksendal. This book was released on 2007-04-26. Applied Stochastic Control of Jump Diffusions available in PDF, EPUB and Kindle. Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.
Stochastic Flows and Stochastic Differential Equations
Stochastic Flows and Stochastic Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Flows and Stochastic Differential Equations write by Hiroshi Kunita. This book was released on 1990. Stochastic Flows and Stochastic Differential Equations available in PDF, EPUB and Kindle. 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. Itô and since then has been much developed. Professor Kunita's approach here is to regard the stochastic differential equation as a dynamical system driven by a random vector field, including thereby Itô's theory as a special case. The book can be used with advanced courses on probability theory or for self-study.
