Stochastic Flows and Jump-Diffusions

Nonfiction, Science & Nature, Mathematics, Applied, Statistics
Cover of the book Stochastic Flows and Jump-Diffusions by Hiroshi Kunita, Springer Singapore
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Hiroshi Kunita ISBN: 9789811338014
Publisher: Springer Singapore Publication: March 26, 2019
Imprint: Springer Language: English
Author: Hiroshi Kunita
ISBN: 9789811338014
Publisher: Springer Singapore
Publication: March 26, 2019
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer Singapore

Cover of the book Translational Research in Breast Cancer by Hiroshi Kunita
Cover of the book Optical Soliton Communication Using Ultra-Short Pulses by Hiroshi Kunita
Cover of the book Sustainable Agriculture towards Food Security by Hiroshi Kunita
Cover of the book Emerging Technologies in Data Mining and Information Security by Hiroshi Kunita
Cover of the book Generalized Inverses: Theory and Computations by Hiroshi Kunita
Cover of the book Sustainable Plantation Forestry by Hiroshi Kunita
Cover of the book Researching Catholic Education by Hiroshi Kunita
Cover of the book Shear Strengthening of T-beam with GFRP by Hiroshi Kunita
Cover of the book Large Floating Structures by Hiroshi Kunita
Cover of the book Governance and Governed by Hiroshi Kunita
Cover of the book Ciliate Atlas: Species Found in the South China Sea by Hiroshi Kunita
Cover of the book Deuteride Materials by Hiroshi Kunita
Cover of the book Employee Voice at Work by Hiroshi Kunita
Cover of the book Variational Continuum Multiphase Poroelasticity by Hiroshi Kunita
Cover of the book Strategic Research on Construction and Promotion of China's Intelligent Cities by Hiroshi Kunita
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy