Stochastic Processes

Selected Papers On Hiroshi Tanaka

By: Makoto Maejima (Editor), Tokuzo Shiga (Editor)

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Hardcover | 4 April 2002

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Hiroshi Tanaka is noted for his discovery of the "Tanaka Formula", which is a generalization of the Ito formula in stochastic analysis. This 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 volume also includes essays by Henry McKean, Marc Yor, Shinzo Watanabe and Hiroshi Tanaka on Tanaka's works.

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Preface
H. Tanaka: An Appreciation	p. 1
From Local Times to Random Environments	p. 2
Contributions and Influences of Professor Tanaka in Stochastic Analysis	p. 5
Some Comments on My Mathematical Works in Retrospect	p. 10
Additive Functionals of the Brownian Path	p. 19
Note on Continuous Additive Functionals of the 1-Dimensional Brownian Path	p. 47
Existence of Diffusions with Continuous Coefficients	p. 54
Propagation of Chaos for Certain Purely Discontinuous Markov Processes with Interactions	p. 69
An Inequality for a Functional of Probability Distributions and Its Application to Kac's One-Dimensional Model of a Maxwellian Gas	p. 83
On Markov Process Corresponding to Boltzmann's Equation of Maxwellian Gas	p. 89
On the Uniqueness of Markov Process Associated with the Boltzmann Equation of Maxwellian Molecules	p. 101
Probabilistic Treatment of the Boltzmann Equation of Maxwellian Molecules	p. 118
Stochastic Differential Equations with Reflecting Boundary Condition in Convex Regions	p. 157
Some Probabilistic Problems in the Spatially Homogeneous Boltzmann Equation	p. 172
Limit Theorems for Certain Diffusion Processes with Interaction	p. 182
Central Limit Theorem for a System of Markovian Particles with Mean Field Interactions	p. 202
Propagation of Chaos for Diffusing Particles of Two Types with Singular Mean Field Interaction	p. 223
Stochastic Differential Equations for Mutually Reflecting Brownian Balls	p. 238
Limit Distribution for 1-Dimensional Diffusion in a Reflected Brownian Medium	p. 254
Limit Distributions for One-Dimensional Diffusion Processes in Self-Similar Random Environments	p. 270
Stochastic Differential Equation Corresponding to the Spatially Homogeneous Boltzmann Equation of Maxwellian and Non-Cutoff Type	p. 292
Limit Theorem for One-Dimensional Diffusion Process in Brownian Environment	p. 311
On the Maximum of a Diffusion Process in a Drifted Brownian Environment	p. 328
Recurrence of a Diffusion Process in a Multidimensional Brownian Environment	p. 336
Localization of a Diffusion Process in a One-Dimensional Brownian Environment	p. 341
Diffusion Processes in Random Environments	p. 353
Environment-Wise Central Limit Theorem for a Diffusion in a Brownian Environment with Large Drift	p. 361
A Diffusion Process in a Brownian Environment with Drift	p. 373
Limit Theorems for a Brownian Motion with Drift in a White Noise Environment	p. 396
Invariance Principle for a Brownian Motion with Large Drift in a White Noise environment	p. 406
Some Theorems Concerning Extrema of Brownian Motion with d-Dimensional Time	p. 415
Bibliography of Hiroshi Tanaka	p. 425
Permissions	p. 429
Table of Contents provided by Blackwell. All Rights Reserved.

Stochastic Processes

Selected Papers On Hiroshi Tanaka

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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