Bounds for the expected supremum of some non-stationary Gaussian processes

Abstract

The aim of this article is to obtain closed-form lower and upper bounds for the expectation of the supremum of some non-stationary Gaussian processes. This supremum is an important quantity in applications such as finance and queueing systems. The covariance function structure, decomposition of the processes and probability inequalities are applied for some examples of non-stationary Gaussian processes, including sub-fractional, bifractional and multifractional Brownian motions. Malliavin calculus operators are also applied in some cases to find bounds for the density and expectation of the supremum of these processes.