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On the supremum of certain families of stochastic processes

Author

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

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.

Suggested Citation

  • Li, Wenbo V. & Pillai, Natesh S. & Wolpert, Robert L., 2010. "On the supremum of certain families of stochastic processes," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 916-921, June.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:11-12:p:916-921
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    References listed on IDEAS

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    1. Reynaud-Bouret, P., 2006. "Compensator and exponential inequalities for some suprema of counting processes," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1514-1521, August.
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