Journal of Applied Mathematics and Stochastic Analysis
Volume 12 (1999), Issue 2, Pages 133-150
Existence of moments of increasing predictable processes associated with one- and two-parameter potentials
Kiev University, Department of Mathematics, Kiev 252601, Ukraine
Received 1 March 1997; Revised 1 May 1998
Copyright © 1999 Yu. Mishura and Ya. Oltsik. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The criterion and sufficient condition for the existence of moments of one-parameter increasing predictable processes is presented in terms of an associated potential. The estimates of moments of special functional connected with two-parameter increasing predictable processes are given in the
case when the associated potential is bounded. The application of these
estimates to the local time for purely discontinuous strong martingales in
the plane is also presented.