On the Probability of Conjunctions of Stationary Gaussian Processes

Abstract

Let $\{X_i(t),t\ge 0\},1\le i\le n$ be independent centered stationary Gaussian processes with unit variance and almost surely continuous sample paths. For given positive constants $u,T$, define the set of conjunctions $C_{[0,T],u}:=\{t\in [0,T]:{\min }_{1\le i\le n}{X}_i(t)\ge u\}.$ Motivated by some applications in brain mapping and digital communication systems, we obtain exact asymptotic expansion of $P(C_{[0,T],u}\ne \phi )$ as $u\to \infty$. Moreover, we establish the Berman sojourn limit theorem for the random process $\{{\min }_{1\le i\le n}{X}_i(t),t\ge 0\}$ and derive the tail asymptotics of the supremum of each order statistics process.

11 pages, Theorem 2.3 is new in this version

References in corpus (1)

• Tail Asymptotics of Supremum of Certain Gaussian Processes over Threshold Dependent Random Intervals

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