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Contents of PMS, Vol. 16, Fasc. 2,
pages 243 - 260
 

AUTOREGRESSIVE LAPLACE 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 n t of the random Laplace functional integral oo exp(- tX(t,w))dt 0 for t > 0. In particular, a necessary and sufficient condition in terms of corresponding representing measures for n , t to be multiplicatively autoregressive is established.

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

Key words and phrases: -

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