Stochastic processes : selected papers of Hiroshi Tanaka / edited by Makoto Maejima, Tokuzo Shiga.

Format:

Book

Author/Creator:

Tanaka, Hiroshi.

Contributor:

Maejima, Makoto.

Shiga, Tokuzo.

Language:

English

Subjects (All):

Stochastic processes.

Tanaka, Hiroshi.

Physical Description:

1 online resource (xi, 430 p. ) port.

Edition:

1st ed.

Place of Publication:

River Edge, N.J. : World Scientific, c2002.

Language Note:

English

Summary:

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

Contents:

Machine generated contents note: 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 (with T. Shiga)

Propagation of Chaos for Diffusing Particles of Two Types with Singular Mean Field Interaction (with M. Nagasawa)

Stochastic Differential Equations for Mutually Reflecting Brownian Balls (with Y. Saisho)

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 (with K. Kawazu)

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 (with K. Kawazu)

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 (with K. Kawazu)

Some Theorems Concerning Extrema of Brownian Motion with d-Dimensional Time.

Notes:

Bibliographic Level Mode of Issuance: Monograph

"Bibliography of Hiroshi Tanaka": p. 425-430.

Includes bibliographical references.

ISBN:

9789812778550

9812778551

OCLC:

879025340