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 M _{1}-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 |