Stochastic Flows and Jump-Diffusions (eBook)

Hiroshi Kunita (Autor)

eBook Download: PDF

2019 | 1st ed. 2019
XVII, 352 Seiten
Springer Singapore (Verlag)
978-981-13-3801-4 (ISBN)

Infos

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.

Kunita was an invited speaker at the ICM 1986. 

Inhalt

Preface.- Introduction.- 1.Probability distributions and stochastic processes.- 2.Stochastic integrals based on Wiener processes and Poisson random measures.- 3.Stochastic differential equations and stochastic flows.- 4.Diffusions, jump-diffusions and heat equations.- 5.Malliavin calculus for Wiener processes and Poisson random measures.- 6.Smooth densities and heat kernels.- 7.Jump-diffusions on manifolds and smooth densities.- Bibliography.- Index.

Produkt-Details

• Erscheint lt. Verlag: 26.3.2019
• Reihe/Serie: Probability Theory and Stochastic Modelling
• Reihe/Serie: Probability Theory and Stochastic Modelling
• Zusatzinfo: XVII, 352 p. 145 illus.
• Verlagsort: Singapore
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Recht / Steuern ► Wirtschaftsrecht
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management
• Schlagworte: 35K08, 35K10, 58J05 • 60H05, 60H07, 60H30 • asymptotic short time estimate • backward heat equations • diffeomorphism • diffusion and jump-diffusion processes • fundamental solution • heat equations • jump-diffusion process • Malliavin calculus • Partial differential equations • Quantitative Finance • smooth density • stochastic differential equation with jumps • stochastic flow • Wiener space
• ISBN-10: 981-13-3801-9 / 9811338019
• ISBN-13: 978-981-13-3801-4 / 9789811338014