Ebook: Prokhorov and Contemporary Probability Theory: In Honor of Yuri V. Prokhorov

The role of Yuri Vasilyevich Prokhorov as a prominent mathematician and leading expert in the theory of probability is well known. Even early in his career he obtained substantial results on the validity of the strong law of large numbers and on the estimates (bounds) of the rates of convergence, some of which are the best possible. His findings on limit theorems in metric spaces and particularly functional limit theorems are of exceptional importance. Y.V. Prokhorov developed an original approach to the proof of functional limit theorems, based on the weak convergence of finite dimensional distributions and the condition of tightness of probability measures.

The present volume commemorates the 80^th birthday of Yuri Vasilyevich Prokhorov. It includes scientific contributions written by his colleagues, friends and pupils, who would like to express their deep respect and sincerest admiration for him and his scientific work.​

The role of Yuri Vasilyevich Prokhorov as a prominent mathematician and leading expert in the theory of probability is well known. Even early in his career he obtained substantial results on the validity of the strong law of large numbers and on the estimates (bounds) of the rates of convergence, some of which are the best possible. His findings on limit theorems in metric spaces and particularly functional limit theorems are of exceptional importance. Y.V. Prokhorov developed an original approach to the proof of functional limit theorems, based on the weak convergence of finite dimensional distributions and the condition of tightness of probability measures.

The present volume commemorates the 80^th birthday of Yuri Vasilyevich Prokhorov. It includes scientific contributions written by his colleagues, friends and pupils, who would like to express their deep respect and sincerest admiration for him and his scientific work.?

The role of Yuri Vasilyevich Prokhorov as a prominent mathematician and leading expert in the theory of probability is well known. Even early in his career he obtained substantial results on the validity of the strong law of large numbers and on the estimates (bounds) of the rates of convergence, some of which are the best possible. His findings on limit theorems in metric spaces and particularly functional limit theorems are of exceptional importance. Y.V. Prokhorov developed an original approach to the proof of functional limit theorems, based on the weak convergence of finite dimensional distributions and the condition of tightness of probability measures.

The present volume commemorates the 80^th birthday of Yuri Vasilyevich Prokhorov. It includes scientific contributions written by his colleagues, friends and pupils, who would like to express their deep respect and sincerest admiration for him and his scientific work.?

Content:
Front Matter....Pages i-xxxviii
Front Matter....Pages 1-1
When Knowing Early Matters: Gossip, Percolation and Nash Equilibria....Pages 3-27
A Mathematical Model of Investment Incentives....Pages 29-41
The Shape of Asymptotic Dependence....Pages 43-67
Limit Theorems for Functionals of Higher Order Differences of Brownian Semi-Stationary Processes....Pages 69-96
Retrieving Information from Subordination....Pages 97-106
Asymptotic Expansions for Distributions of Sums of Independent Random Vectors....Pages 107-125
An Extension of the Concept of Slowly Varying Function with Applications to Large Deviation Limit Theorems....Pages 127-139
Optimal and Asymptotically Optimal Control for Some Inventory Models....Pages 141-162
Levy Preservation and Associated Properties for f -Divergence Minimal Equivalent Martingale Measures....Pages 163-196
Non-standard Limit Theorems in Number Theory....Pages 197-213
Additive Functions and Gaussian Measures....Pages 215-223
Free Infinitely Divisible Approximations of n-Fold Free Convolutions....Pages 225-237
Accurate Approximation of Correlation Coefficients by Short Edgeworth-Chebyshev Expansion and Its Statistical Applications....Pages 239-260
The Stein-Tikhomirov Method and Berry-Esseen Inequality for Sampling Sums from a Finite Population of Independent Random Variables....Pages 261-273
On One Inequality for Characteristic Functions....Pages 275-280
On the Nonlinear Filtering Equations for Superprocesses in Random Environment....Pages 281-291
Upper Bounds for Bernstein Basis Functions....Pages 293-301
On Distribution of Zeros of Random Polynomials in Complex Plane....Pages 303-323
Dependence and Interaction in Branching Processes....Pages 325-333
Testing Functional Connection between Two Random Variables....Pages 335-348
Front Matter....Pages 1-1
Solution of the Optimal Stopping Problem for One-Dimensional Diffusion Based on a Modification of the Payoff Function....Pages 349-369
Front Matter....Pages 371-403
The Times of Yuri Vasilyevich Prokhorov....Pages 405-405
A Conversation with Yuri Vasilyevich Prokhorov....Pages 407-431
....Pages 433-446