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

ISBN-13: 9783642431685 / Angielski / Miękka / 2015 / 446 str.

Ernst L Presman;S R S Varadhan;Albert N Shiryaev

Opis

The role of Yuri Vasilyevich Prokhorov as a prominent mathematician and leading expert in the theory of probability is well known. 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.

Spis treści

Part I Scientific Papers: David J. Aldous: When Knowing Early Matters: Gossip, Percolation and Nash Equilibria.- Vadim Arkin and Alexander Slastnikov: A Mathematical Model of Investment Incentives.- Guus Balkema, Paul Embrechts and Natalia Nolde: The Shape of Asymptotic Dependence.- Ole E. Barndorff-Nielsen, Jose Manuel Corcuera and Mark Podolskij: Limit theorems for functionals of higher order differences of Brownian semi-stationary processes.-  Jean Bertoin and Marc Yor: Retrieving Information from Subordination.- Algimantas Bikelis: Asymptotic Expansions for Distributions of Sums of Independent Random Vectors.-  Alexandr A. Borovkov and Konstantin A. Borovkov: An Extension of the Concept of Slowly Varying Function with Applications to Large Deviation Limit Theorems.- Ekaterina Bulinskaya: Optimal and Asymptotically Optimal Control for Some Inventory Models.- Suzanne Cawston and Lioudmila Vostrikova: Levy Preservation and Associated Properties for f -divergence Minimal Equivalent Martingale Measures.- Francesco Cellarosi, Yakov G. Sinai: Non-Standard Limit Theorems in Number Theory.- Linan Chen and Daniel W. Stroock: Additive Functions and Gaussian Measures.- Gennadii Chistyakov and Friedrich Gotze: Free Infinitely Divisible Approximations of n-fold Free Convolutions.- Gerd Christoph, Vladimir V. Ulyanov and Yasunori Fujikoshi: Accurate Approximation of  Correlation Coefficients by Short Edgeworth-Chebyshev Expansion and Its Statistical Applications.-  Shakir K. Formanov and Tamara A. Formanova: The Stein-Tikhomirov Method and Berry-Esseen Inequality for Sampling Sums from a Finite Population of Independent Random Variables.- Nicko Gamkrelidze: On One Inequality for Characteristic Functions.- Bronius Grigelionis: On the Nonlinear Filtering Equations for Superprocesses in Random Environment.- Vijay Gupta and Tengiz Shervashidze: Upper Bounds for Bernstein Basis Functions.-  Ildar Ibragimov and Dmitry Zaporozhets: On Distribution of Zeros of Random Polynomials in Complex Plane.- Peter Jagers and Fima C. Klebaner: Dependence and Interaction in Branching Processes.-  Gyula O.H. Katona: Testing Functional Connection between Two Random Variables.- Kalyanapuram R.Parthasarathy: The Symmetry Group of Gaussian States in L2(Rn).-  Ernst Presman: Solution of the Optimal Stopping Problem for One-dimensional Diffusion Based on a Modification of the Payoff Function.- Part II Interviews: Friedrich Götze and Willem R. van Zwet: The times of Yuri Vasilyevich Prokhorov.- Larry Shepp: A Conversation with Yuri Vasilyevich Prokhorov.​    

 

Blurb

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.​