Skorokhod volume

Skorokhod's Ideas in Probability Theory

This volume, a collection of research papers published in English, 336 pp., is issued in 2000 by the Institute of Mathematics of the National Academy of Sciences of Ukraine, eds: V.Korolyuk, N.Portenko, H.Syta.

The volume is issued on occasion of the 70-th anniversary of A.V.Skorokhod's birthday.

The scientific papers of this volume are connected with either notions introduced into Probability Theory by A.V.Skorokhod or methods proposed by him for solving various problems of this science. A considerable part of the volume concerns the first outstanding work written by A.V.Skorokhod "Limit theorems for stochastic processes" (Theory Probab. Appl., 1956, Vol. 1, No. 3), - the work in which he proposed the method of a single probability space and introduced several topologies into the space of all functions without discontinuities of the second kind, and proved some limit theorems that were the deep generalization of the famous Donsker invariant principle.

Besides scientific papers, the volume contains the main landmarks of A.V.Skorokhod's biography, the list of his monographs, textbooks and popular-science books, and illustrated by some photos.

The volume may be useful for the experts in Probability Theory and its applications, and is accessible for post-graduates and magister degree students.

Persons and institutions wishing to order the volume should appeal to the following e-mail address:

random@imath.kiev.ua

or by the ordinary mail to the address:

        Random Process Dept.
        Institute of Mathematics
        Nat. Acad. Sci. Ukraine
        3, Tereshchenkivska str,.
        01601, Kyiv-4
        Ukraine

The price of the book (postage included) is US $35.

The amount has to be payed by bank transfer to:

        30-31-4 Credit Suise Bank
        Berne, Switzerland
        Voronoi Fund
        0207-143954-90-3

Contents Pages
Preface 11-12
Main Landmarks of Anatolii Skorokhod's Life 13-14
Monograghs, Textbooks, Reference Books and Popular-Science books Written by A.V.Skorokhod 15-19
A Few Words about the Teacher 20-21
Anatolii V. SKOROKHOD
Limit Theorems for Stochastic Processes 23-52
Andrey N. KOLMOGOROV
On Skorokhod Convergence 53-60
Patrick BILLINGSLEY and Michel WICHURA
The Origins of Skorokhod's Topology 61-65
Robert F. ANDERSON and Stanislav MOLCHANOV
Martingale Methods in Real Analysis 66-80
Vladimir V. ANISIMOV
J-Convergence of Switching Processes with Rare Perturbations to Diffusion Processes with Poisson Type Jumps 81-98
Mindaugas BLOZNELIS and Vygantas PAULAUSKAS
Central Limit Theorem in D[0,1] 99-110
George L. O'BRIEN
An Application of Skorokhod's M₁-topology 111-118
Sergei A.CHOBANYAN and Habib SALEHI
A Maximal Inequality for Exchangeable Systems of Random Variables 119-125
Francois COQUET and Michel GUILLEMEAU
A Remark on Skorokhod Topologies for the Skorokhod Reflexion Problem 126-131
Yurii L. DALETSKII and Victoria R. STEBLOVSKAYA
Measures with Smooth Finite-Dimensional Projections 132-146
Andrey A. DOROGOVTSEV
The Variant of the Skorokhod Theorem for Markovian Sequences 147-151
Bronius GRIGELIONIS
Mixed Exponential Processes 152-171
B.Gail IVANOFF and Ely MERZBACH
A Skorokhod Topology for a Class of Set-Indexed Functions 172-178
Adam JAKUBOWSKI
From Convergence of Functions to Convergence of Stochastic Processes. On Skorokhod's Sequential Approach to Convergence in Distribution 179-194
Vladimir KOLTCHINSKII and Richard M.DUDLEY
On Spatial Quantiles 195-210
Peter KOTELENEZ
Smooth Solutions of Quasilinear Stochastic Partial Differential Equations of McKean-Vlasov Type 211-231
Nikolai V. KRYLOV
Constructing the Super-Brownian Process by Using SPDE's and Skorokhod's Method 232-240
Grigori L. KULINICH and Murad ALMAZOV
On Convergence of Solutions of Stochastic Diffusion Equations with Unlimited Increasing Drift Coefficient on Finite Segment 241-247
Hui-Hsiung KUO
Anticipatory Ito's Formula and Hitsuda-Skorokhod Integral 248-255
Robert LIPTSER
Moderate Deviation for Dynamic Model Governed by Stationary Process 256-270
Sergey V. LOTOTSKY and Boris L. ROSOVSKII
Parameter Estimation for Stochastic Evolution Equations with Non-Commuting Operators 271-280
Yuliya MISHURA
Skorokhod Space and Skorokhod Topology in Probabilistic Considerations During 1956 - 1999 281-297
Dmitrii S. SILVESTROV
Convergence in Skorokhod Topology for Compositions of Stochastic Processes 298-306
Veeravalli S. VARADARAJAN
Remarks on Some Applications of Skorokhod Space in Quantum Mechanics 307-312
Andriy P. YURACHKIVSKY
Functional Limit Theorems with Poisson Component for the Measure of Union of Random Sets 313-317
Weian ZHENG
Rate Estimation for Weak Convergence of Diffusion Processes 318-333

Contents	Pages
Preface	11-12
Main Landmarks of Anatolii Skorokhod's Life	13-14
Monograghs, Textbooks, Reference Books and Popular-Science books Written by A.V.Skorokhod	15-19
A Few Words about the Teacher	20-21
Anatolii V. SKOROKHOD Limit Theorems for Stochastic Processes	23-52
Andrey N. KOLMOGOROV On Skorokhod Convergence	53-60
Patrick BILLINGSLEY and Michel WICHURA The Origins of Skorokhod's Topology	61-65
Robert F. ANDERSON and Stanislav MOLCHANOV Martingale Methods in Real Analysis	66-80
Vladimir V. ANISIMOV J-Convergence of Switching Processes with Rare Perturbations to Diffusion Processes with Poisson Type Jumps	81-98
Mindaugas BLOZNELIS and Vygantas PAULAUSKAS Central Limit Theorem in D[0,1]	99-110
George L. O'BRIEN An Application of Skorokhod's M₁-topology	111-118
Sergei A.CHOBANYAN and Habib SALEHI A Maximal Inequality for Exchangeable Systems of Random Variables	119-125
Francois COQUET and Michel GUILLEMEAU A Remark on Skorokhod Topologies for the Skorokhod Reflexion Problem	126-131
Yurii L. DALETSKII and Victoria R. STEBLOVSKAYA Measures with Smooth Finite-Dimensional Projections	132-146
Andrey A. DOROGOVTSEV The Variant of the Skorokhod Theorem for Markovian Sequences	147-151
Bronius GRIGELIONIS Mixed Exponential Processes	152-171
B.Gail IVANOFF and Ely MERZBACH A Skorokhod Topology for a Class of Set-Indexed Functions	172-178
Adam JAKUBOWSKI From Convergence of Functions to Convergence of Stochastic Processes. On Skorokhod's Sequential Approach to Convergence in Distribution	179-194
Vladimir KOLTCHINSKII and Richard M.DUDLEY On Spatial Quantiles	195-210
Peter KOTELENEZ Smooth Solutions of Quasilinear Stochastic Partial Differential Equations of McKean-Vlasov Type	211-231
Nikolai V. KRYLOV Constructing the Super-Brownian Process by Using SPDE's and Skorokhod's Method	232-240
Grigori L. KULINICH and Murad ALMAZOV On Convergence of Solutions of Stochastic Diffusion Equations with Unlimited Increasing Drift Coefficient on Finite Segment	241-247
Hui-Hsiung KUO Anticipatory Ito's Formula and Hitsuda-Skorokhod Integral	248-255
Robert LIPTSER Moderate Deviation for Dynamic Model Governed by Stationary Process	256-270
Sergey V. LOTOTSKY and Boris L. ROSOVSKII Parameter Estimation for Stochastic Evolution Equations with Non-Commuting Operators	271-280
Yuliya MISHURA Skorokhod Space and Skorokhod Topology in Probabilistic Considerations During 1956 - 1999	281-297
Dmitrii S. SILVESTROV Convergence in Skorokhod Topology for Compositions of Stochastic Processes	298-306
Veeravalli S. VARADARAJAN Remarks on Some Applications of Skorokhod Space in Quantum Mechanics	307-312
Andriy P. YURACHKIVSKY Functional Limit Theorems with Poisson Component for the Measure of Union of Random Sets	313-317
Weian ZHENG Rate Estimation for Weak Convergence of Diffusion Processes	318-333