On the Supremum of Certain Families of Stochastic Processes

Details On the Supremum of Certain Families of Stochastic Processes On the Supremum of Certain Families of Stochastic Processes

2008-12-21

arxiv.org/abs/0812.4062v2

Mathematics

Probability

Referee comments incorporated, the main result is stated in a more general form

Scientific paper

We consider a family of stochastic processes $\{X_t^\epsilon, t \in T\}$ on a metric space $T$, with a parameter $\epsilon \downarrow 0$. We study the conditions under which \lim_{\e \to 0} \P \Big(\sup_{t \in T} |X_t^\e| < \delta \Big) =1 when one has the \textit{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 intergrals with respect to compound Poisson random measures with infinite intensity measures.

Affiliated with

Also associated with

No associations

Rating

On the Supremum of Certain Families of Stochastic Processes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Supremum of Certain Families of Stochastic Processes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Supremum of Certain Families of Stochastic Processes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-537539