UNIVERSITY
OF WROCŁAW
 
Main Page
Contents of previous volumes
Forthcoming papers
General Information
Instructions for authors


VOLUMES
38.2 38.1 37.2 37.1 36.2 36.1 35.2
35.1 34.2 34.1 33.2 33.1 32.2 32.1
31.2 31.1 30.2 30.1 29.2 29.1 28.2
28.1 27.2 27.1 26.2 26.1 25.2 25.1
24.2 24.1 23.2 23.1 22.2 22.1 21.2
21.1 20.2 20.1 19.2 19.1 18.2 18.1
17.2 17.1 16.2 16.1 15 14.2 14.1
13.2 13.1 12.2 12.1 11.2 11.1 10.2
10.1 9.2 9.1 8 7.2 7.1 6.2
6.1 5.2 5.1 4.2 4.1 3.2 3.1
2.2 2.1 1.2 1.1
 
 
WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 5, Fasc. 1,
pages 45 - 58
 

ON RECURRENT DIFFERENTIAL REPRESENTATIONS FOR STATIONARY STOCHASTIC PROCESSES

Lesław Bielak

Abstract: In this paper differential representations for stationary stochastic processes with quotients of analytic functions of minimal type as spectral characteristics are given. Such a process is a limit (in the mean square sense) of stationary stochastic processes y (t)
 n (n = 1,2,...) which are solutions of an infinite-dimensional system of stochastic differential equations. There are some recurrent connections between y (t)
 n and for that reason we call the differential representations considered in this paper recurrent. The representations are applied to find a necessary and sufficient condition for absolute Continuity of measures generated by Gaussian stationary processes with spectral characteristics mentioned above. This condition takes the form

    gy(c)
cli-->m oo  gx(c) = 1.
Thereby the Feldman theorem is generalized.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

Download:    Abstract    Full text   Abstract + References