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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 15, Fasc. ,
pages 493 - 513
 

INFINITE DIVISIBILITY OF SOME FUNCTIONALS ON STOCHASTIC PROCESSES

K. Urbanik

Abstract: The paper deals with non-negative stochastic processes X(t,w) (t > 0) with stationary and independent increments, continuous on the right sample functions, non-degenerate to 0 and fulfilling the initial condition X(0,w) = 0. The main aim is to study the probability distribution of the functional integral oo e-uX(t,w)dt 0 for u > 0. In particular, the multiplicative infinite divisibility of such functionals is discussed and a description of corresponding spectral measures is established.

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

Key words and phrases: -

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