Stochastic Processes: Selected Papers of Hiroshi Tanaka

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World Scientific, 2002 - Mathematics - 430 pages
Hiroshi Tanaka is noted for his discovery of the ?Tanaka formula?, which is a generalization of the It formula in stochastic analysis. This important book is a selection of his brilliant works on stochastic processes and related topics. It contains Tanaka's papers on (i) Brownian motion and stochastic differential equations (additive functionals of Brownian paths and stochastic differential equations with reflecting boundaries), (ii) the probabilistic treatment of nonlinear equations (Boltzmann equation, propagation of chaos and McKean-Vlasov limit), and (iii) stochastic processes in random environments (especially limit theorems on the stochastic processes in one-dimensional random environments and their refinements). The book also includes essays by Henry McKean, Marc Yor, Shinzo Watanabe and Hiroshi Tanaka on Tanaka's works.
 

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Contents

An Appreciation
1
From Local Times to Random Environments
2
Contributions and Influences of Professor Tanaka in Stochastic Analysis
5
Some Comments on My Mathematical Works in Retrospect
10
Additive Functionals of the Brownian Path
19
Note on Continuous Additive Functionals of the 1Dimensional Brownian Path
47
Existence of Diffusions with Continuous Coefficients
54
Propagation of Chaos for Certain Purely Discontinuous Markov Processes with Interactions ...
69
Stochastic Differential Equations for Mutually Reflecting Brownian Balls
238
Limit Distribution for 1Dimensional Diffusion in a Reflected Brownian Medium
254
Limit Distributions for OneDimensional Diffusion Processes in SelfSimilar Random Environments ...
270
Stochastic Differential Equation Corresponding to the Spatially Homogeneous Boltzmann Equation of Maxwellian and NonCutoff Type ...
292
Limit Theorem for OneDimensional Diffusion Process in Brownian Environment
311
On the Maximum of a Diffusion Process in a Drifted Brownian Environment
328
86 Recurrence of a Diffusion Process in a Multidimensional Brownian Environment
336
Localization of a Diffusion Process in a OneDimensional Brownian Environment
341

An Inequality for a Functional of Probability Distributions and Its Application to Kacs OneDimensional Model of a Maxwellian Gas ...
83
On Markov Process Corresponding to Boltzmanns Equation of Maxwellian Gas
89
On the Uniqueness of Markov Process Associated with the Boltzmann Equation of Maxwellian Molecules ...
101
Probabilistic Treatment of the Boltzmann Equation of Maxwellian Molecules
118
Stochastic Differential Equations with Reflecting Boundary Condition in Convex Regions
157
Some Probabilistic Problems in the Spatially Homogeneous Boltzmann Equation
172
Limit Theorems for Certain Diffusion Processes with Interaction
182
Central Limit Theorem for a System of Markovian Particles with Mean Field Interactions
202
Propagation of Chaos for Diffusing Particles of Two Types with Singular Mean Field Interaction ...
223
Diffusion Processes in Random Environments
353
EnvironmentWise Central Limit Theorem for a Diffusion in a Brownian Environment with Large Drift ...
361
A Diffusion Process in a Brownian Environment with Drift
373
Limit Theorems for a Brownian Motion with Drift in a White Noise Environment
396
Invariance Principle for a Brownian Motion with Large Drift in a White Noise Environment ...
406
Some Theorems Concerning Extrema of Brownian Motion with dDimensional Time
415
Bibliography of Hiroshi Tanaka
425
Permissions
429
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