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Tables of Contents for Stochastic Processes
Chapter/Section Title
Page #
Page Count
Preface
vii
An Appreciation
1
1
From Local Times to Random Environments
2
3
Contributions and Influences of Professor Tanaka in Stochastic Analysis
5
5
Some Comments on My Mathematical Works in Retrospect
10
9
Additive Functionals of the Brownian Path
19
28
Note on Continuous Additive Functionals of the 1-Dimensional
47
7
Existence of Diffusions with Continuous Coefficients
54
15
Propagation of Chaos for Certain Purely Discontinuous Markov Processes with Interactions
69
14
An Inequality for a Functional of Probability Distributions and Its Application to Kac's One-Dimensional Model of a Maxwellian Gas
83
6
On Markov Process Corresponding to Boltzmann's Equation of Maxwellian Gas
89
12
On the Uniqueness of Markov Process Associated with the Boltzmann Equation of Maxwellian Molecules
101
17
Probabilistic Treatment of the Boltzmann Equation of Maxwellian Molecules
118
39
Stochastic Differential Equations with Reflecting Boundary Condition in Convex Regions
157
15
Some Probabilistic Problems in the Spatially Homogeneous Boltzmann Equation
172
10
Limit Theorems for Certain Diffusion Processes with Interaction
182
20
Central Limit Theorem for a System of Markovian Particles with Mean Field Interactions
202
21
Propagation of Chaos for Diffusing Particles of Two Types with Singular Mean Field Interaction
223
15
Stochastic Differential Equations for Mutually Reflecting Brownian Balls
238
16
Limit Distribution for 1-Dimensional Diffusion in a Reflected Brownian Medium
254
16
Limit Distributions for One-Dimensional Diffusion Processes in Self-Similar Random Environments
270
22
Stochastic Differential Equation Corresponding to the Spatially Homogeneous Boltzmann Equation of Maxwellian and Non-Cutoff Type
292
19
Limit Theorem for One-Dimensional Diffusion Process in Brownian Environment
311
17
On the Maximum of a Diffusion Process in a Drifted Brownian Environment
328
8
Recurrence of a Diffusion Process in a Multidimensional Brownian Environment
336
5
Localization of a Diffusion Process in a One-Dimensional Brownian Environment
341
12
Diffusion Processes in Random Environments
353
8
Environment-Wise Central Limit Theorem for a Diffusion in a Brownian Environment with Large Drift
361
12
A Diffusion Process in a Brownian Environment with Drift
373
23
Limit Theorems for a Brownian Motion with Drift in a White Noise Environment
396
10
Invariance Principle for a Brownian Motion with Large Drift in a White Noise Environment
406
9
Some Theorems Concerning Extrema of Brownian Motion with d-Dimensional Time
415
10
Bibliography of Hiroshi Tanaka
425
4
Permissions
429