Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1153228 | Statistics & Probability Letters | 2010 | 6 Pages |
Abstract
We consider a family of stochastic processes {Xtϵ,tâT} on a metric space T, with a parameter ϵâ0. We study the conditions under which limϵâ0P(suptâT|Xtϵ|<δ)=1 when one has an a priori estimate on the modulus of continuity and the value at one point. We compare our problem to the celebrated Kolmogorov continuity criteria for stochastic processes, and finally give an application of our main result for stochastic integrals with respect to compound Poisson random measures with infinite intensity measures.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Wenbo V. Li, Natesh S. Pillai, Robert L. Wolpert,