Stochastic Flows and Jump-Diffusions by Hiroshi Kunita
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 heatequations are constructed independently of the theory of partial differential equations.Researchers and graduate student in probability theory will find this book very useful.-
Foundations of Modern Probability
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Geometry of Level Sets of Random Fields, Kac–Rice Formulas, Hermite Expansions and Applications
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Dynamics on Graphs
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Hybrid Switching Diffusions
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Nonlinear Expectations and Stochastic Calculus under Uncertainty
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Probability on Compact Lie Groups
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Measure-Valued Branching Markov Processes
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Pseudo-Regularly Varying Functions and Generalized Renewal Processes
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Stochastic Disorder Problems
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Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes
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Analysis and Approximation of Rare Events
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Random Ordinary Differential Equations and Their Numerical Solution
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Stochastic Evolution Systems
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Ambit Stochastics
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Mathematical Control Theory for Stochastic Partial Differential Equations
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Dirichlet Forms Methods for Poisson Point Measures and Levy Processes
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Lectures on Monte Carlo Theory
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Stochastic Control Theory
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Random Measures, Theory and Applications
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Yosida Approximations of Stochastic Differential Equations in Infinite Dimensions and Applications
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Random Walks in the Quarter Plane
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Stochastic Multi-Stage Optimization
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The Quasispecies Equation and Classical Population Models
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Asymptotic Theory of Weakly Dependent Random Processes
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Stable Convergence and Stable Limit Theorems
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Stochastic Integration in Banach Spaces
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Continuous-Time Markov Decision Processes
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Dynamic Markov Bridges and Market Microstructure
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Limit Theorems for Multi-Indexed Sums of Random Variables
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Markov Renewal and Piecewise Deterministic Processes
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Convex Stochastic Optimization
“The presentation is self-contained, clear and preciseThe book is definitely a must-read for researchers in the field of stochastic flows and stochastic differential equations.” (G. V. Riabov, Mathematical Reviews, October, 2020)
Kunita was an invited speaker at the ICM 1986.
| SKU | Unavailable |
| ISBN 13 | 9789811338007 |
| ISBN 10 | 9811338000 |
| Title | Stochastic Flows and Jump-Diffusions |
| Author | Hiroshi Kunita |
| Series | Probability Theory And Stochastic Modelling |
| Condition | Unavailable |
| Binding Type | Hardback |
| Publisher | Springer Verlag, Singapore |
| Year published | 2019-04-09 |
| Number of pages | 352 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |