On the Supremum of Certain Families of Stochastic Processes

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

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} ¶\Big…