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 The Ecological Era and Classical Chinese Naturalism by Hiroshi Kunita
Cover of the book Low Carbon Pathways for Growth in India by Hiroshi Kunita
Cover of the book Open and Distance Non-formal Education in Developing Countries by Hiroshi Kunita
Cover of the book Mathematics at the Margins by Hiroshi Kunita
Cover of the book Current Advances in Ophthalmic Technology by Hiroshi Kunita
Cover of the book Theoretical and Experimental Aerodynamics by Hiroshi Kunita
Cover of the book Quantitative and Qualitative Factors that Leads to Slip and Fall Incidents by Hiroshi Kunita
Cover of the book Precision Medicine in Gynecology and Obstetrics by Hiroshi Kunita
Cover of the book Software Literacy by Hiroshi Kunita
Cover of the book Science Education Research and Practice in Asia-Pacific and Beyond by Hiroshi Kunita
Cover of the book Refined Ray Tracing inside Single- and Double-Curvatured Concave Surfaces by Hiroshi Kunita
Cover of the book Biological Invasions and Its Management in China by Hiroshi Kunita
Cover of the book Economic Foundations for Social Complexity Science by Hiroshi Kunita
Cover of the book Returning to Primordially Creative Thinking by Hiroshi Kunita
Cover of the book Probiotics in Agroecosystem 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