The finiteness of the first meeting time between a Gaussian jump and a Brownian particles in the fluid

摘要

In this paper, we present more analysis about the finiteness of the first meeting time between Gaussian jump and Brownian particles in the fluid. Rather than using the uniform integrability conditions which are detailed in El-Hadidy [Mod. Phys. Lett. B 33(22) (2019) 1950256], we show the triangular arrays of the random sequence that represents the probable positions of the first meeting at any time t is an element of R+, to get the stronger moment conditions which are sufficient for the finiteness of this time.