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Name: Lanpeng Ji

Talk Title: Extrema of multi-dimensional Gaussian processes over random intervals

Abstract: Consider an n-dimensional Gaussian process where each coordinate is a Gaussian process with stationary increments and with a (positive or negative) linear drift, and all the coordinates are assumed to be independent. We shall discuss the joint tail asymptotics of the extrema of this multi-dimensional Gaussian process over random intervals, say [0,T_1], [0,T_2],…,[0,T_n], respectively, where T=(T_1,T_2,…,T_n) is a regularly varying random vector which is independent of the Gaussian processes. Our result shows that the structure of the joint tail asymptotics is determined by the signs of the drifts. As a relevant application, we shall discuss a multi-dimensional regenerative model, which is a process with a random alternating environment, where an independent multi-dimensional fractional Brownian motion (fBm) with drift is assigned at each environment alternating time. We derive the corresponding ruin probability by analysing a related perturbed random walk. This is a joint work with Dr Xiaofan Peng (University of Electronic Science and Technology of China).

This talk is a contributed talk at EVA 2021.