Speaker
Description
Self-intersection local times of a random process are random variables describing how much time the process spends in small neighbourhoods of points where the trajectory intersects itself a multiple number of times. Le Gall’s classical result on the asymptotic expansion of the planar Wiener sausage (1990) shows that self-intersection local times are geometric characteristics of random processes describing its topological complexity. It is widely used for the construction of continuous polymer models helping to define polymer measures penalising trajectories with many self-intersections highlighting the excluded volume effect of real polymers.
In this talk, self-intersection local times are discussed for Volterra Gaussian processes. Volterra Gaussain process is defined as a stochastic integral of a deterministic Volterra kernel with respect to a Wiener process. The existence of self-intersection local times for Volterra Gaussian processes is discussed in terms of conditions on Volterra kernels generating processes. Moreover, the aymptotics of conditional moments for self-intersection local times of some classes of Volterra Gaussian processes is described given the end-to-end distance tends to infinity.
