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Catalogue Information
Field name
Details
Dewey Class
519.2
Title
Stochastic Flows and Jump-Diffusions ([EBook] /) / by Hiroshi Kunita.
Author
Kunita, Hiroshi
Other name(s)
SpringerLink (Online service)
Edition statement
1st ed. 2019.
Publication
Singapore : : Springer Singapore : : Imprint: Springer, , 2019.
Physical Details
XVII, 352 p. 145 illus. : online resource.
ISBN
9789811338014
Summary Note
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.:
Contents note
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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site
https://doi.org/10.1007/978-981-13-3801-4
Links to Related Works
Subject References:
Economics, Mathematical
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Partial differential equations
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Probabilities
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Probability theory and stochastic processes
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Quantitative Finance
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Authors:
author
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Kunita, Hiroshi
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Corporate Authors:
SpringerLink (Online service)
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Series:
Probability Theory and Stochastic Modelling
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Classification:
519.2
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