Suppose $X(t),t\in[0,\infty)$ is a centered gaussian process with covariance function $\Gamma(t,s)$, such that $\Gamma(t,t)$ is uniformly bounded over $t\in[0,\infty)$, and $\Gamma(t,t)\rightarrow 0$ as $t\rightarrow\infty$. Is it true that $\sup_{t\in[0,\infty)} |X(t)|$ is $O_p(1)$? Or is some decay rate for the variance required for the supremum to be $O_p(1)$?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.