Inequalities for Increments of Stochastic Processes and Moduli of Continuity
Inequalities for Increments of Stochastic Processes and Moduli of Continuity
Let $\{\Gamma(t), t \in \mathbb{R}\}$ be a Banach space $\mathscr{B}$-valued stochastic process. Let $P$ be the probability measure generated by $\Gamma(\cdot)$. Assume that $\Gamma(\cdot)$ is $P$-almost surely continuous with respect to the norm $\| \|$ of $\mathscr{B}$ and that there exists a positive nondecreasing function $\sigma(a), a > 0$, such …