Stochastic Processes: Selected Papers On Hiroshi Tanaka

Selected Papers of Hiroshi Tanaka

Makoto Maejima, Tokuzo Shiga

• Publisher: World Scientific
• Year: 2002
• Print ISBN: 9789810245917, 9789810245917
• eBook ISBN: 9789812778550
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

Hiroshi Tanaka is noted for his discovery of the "Tanaka formula", which is a generalization of the Itô 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.

Table of contents

• Contents
• Preface
• H. Tanaka: An Appreciation
• From Local Times to Random Environments...
• Contributions and Influences of Professor Tanaka in Stochastic Analysis
• Some Comments on My Mathematical Works in Retrospect
• Additive Functionals of the Brownian Path
• Note on Continuous Additive Functionals of the 1-Dimensional Brownian Path
• Existence of Diffusions with Continuous Coefficients
• Propagation of Chaos for Certain Purely Discontinuous Markov Processes with Interactions
• An Inequality for a Functional of Probability Distributions and Its Application to Kac's One-Dimensional Model of a Maxwellian Gas
• On Markov Process Corresponding to Boltzmann's Equation of Maxwellian Gas
• On the Uniqueness of Markov Process Associated with the Boltzmann Equation of Maxwellian Molecules
• Probabilistic Treatment of the Boltzmann Equation of Maxwellian Molecules
• Stochastic Differential Equations with Reflecting Boundary Condition in Convex Regions
• Some Probabilistic Problems in the Spatially Homogeneous Boltzmann Equation
• Limit Theorems for Certain Diffusion Processes with Interaction
• Central Limit Theorem for a System of Markovian Particles with Mean Field Interactions
• Propagation of Chaos for Diffusing Particles of Two Types with Singular Mean Field Interaction
• Stochastic Differential Equations for Mutually Reflecting Brownian Balls
• Limit Distribution for 1-Dimensional Diffusion in a Reflected Brownian Medium
• Limit Distributions for One-Dimensional Diffusion Processes in Self-Similar Random Environments
• Stochastic Differential Equation Corresponding to the Spatially Homogeneous Boltzmann Equation of Maxwellian and Non-Cutoff Type
• Limit Theorem for One-Dimensional Diffusion Process in Brownian Environment
• On the Maximum of a Diffusion Process in a Drifted Brownian Environment
• 86. Recurrence of a Diffusion Process in a Multidimensional Brownian Environment
• Localization of a Diffusion Process in a One-Dimensional Brownian Environment
• Diffusion Processes in Random Environments
• Environment-Wise Central Limit Theorem for a Diffusion in a Brownian Environment with Large Drift
• A Diffusion Process in a Brownian Environment with Drift
• Limit Theorems for a Brownian Motion with Drift in a White Noise Environment
• Invariance Principle for a Brownian Motion with Large Drift in a White Noise Environment
• Some Theorems Concerning Extrema of Brownian Motion with d-Dimensional Time
• Bibliography of Hiroshi Tanaka
• Permissions