SOME CHARACTERS OF A CLASS OF ORNSTEIN-UHLENBECK TYPE MARKOV PROCESSES WITH STABLE PROCESSES

Acta mathematica scientia,Series B ›› 1997, Vol. 17 ›› Issue (2): 121-128.

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SOME CHARACTERS OF A CLASS OF ORNSTEIN-UHLENBECK TYPE MARKOV PROCESSES WITH STABLE PROCESSES

Wang Yongjin

Department of Mathematics, Nankai University, Tianjin 500071, China

Received:1995-01-03 Revised:1995-05-16 Online:1997-06-25 Published:1997-06-25
Supported by:
Research supported by the Natural Science Foundation of P.R.China

Abstract

Abstract: This article concerns a class of Ornstein-Uhlenbeck type Markov processes and for which the level sets will be approached. By constructing a new class f processes,we shall obtain an inequality on the Hausdorff dimensions of the level sets for the Ornstein-Uhlenbeck type Markov processes. Based on this result, we finally verify that any two independent O-U.M.P with α-stable processes could collide with probability one.

Key words: α-stable process, Ornstein-Uhlenbeck type Markov process, Range, Hausdorff dimension, collision

Wang Yongjin. SOME CHARACTERS OF A CLASS OF ORNSTEIN-UHLENBECK TYPE MARKOV PROCESSES WITH STABLE PROCESSES[J].Acta mathematica scientia,Series B, 1997, 17(2): 121-128.

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SOME CHARACTERS OF A CLASS OF ORNSTEIN-UHLENBECK TYPE MARKOV PROCESSES WITH STABLE PROCESSES

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