On the supremum of certain families of stochastic processes

Wenbo V. Li, Natesh S. Pillai and Robert L. Wolpert

Statistics & Probability Letters, 2010, vol. 80, issue 11-12, 916-921

Abstract: We consider a family of stochastic processes on a metric space T, with a parameter [epsilon][downwards arrow]0. We study the conditions under which 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: Compensated; Poisson; random; measure; Generic; chaining; Kolmogorov; continuity; criterion; Metric; entropy; Suprema; of; stochastic; processes (search for similar items in EconPapers)
Date: 2010
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