Consider a Gaussian process {Xt}t∈T for some index set T . This is a collection of jointly Gaussian random variables, meaning that every finite linear combination of the variables has a Gaussian distribution. We will additionally assume that the process is centered, i.e. E(Xt) = 0 for all t ∈ T . It is well-known that such a process is completely characterized by the covariances {E(XsXt)}s,t∈T ...

Let {Xn}n≥1 be a sequence of i.i.d. standard Gaussian random variables, let Sn = ∑n i=1 Xi be the Gaussian random walk, and let Tn = ∑n i=1 Si be the integrated (or iterated) Gaussian random walk. In this paper we derive the following upper and lower bounds for the conditional persistence: P { max 1≤k≤n Tk ≤ 0 ∣∣∣ Tn = 0, Sn = 0} . n, P { max 1≤k≤2n Tk ≤ 0 ∣∣∣ T2n = 0, S2n = 0} & n−1/2 logn , f...

We consider the problem of optimal allocation of computing budget to maximize the probability of correct selection in the ordinal optimization setting. This problem has been studied in the literature in an approximate mathematical framework under the assumption that the underlying random variables from each population are independent and identically distributed with a Gaussian distribution. We ...