Analytical study of the first collision time finiteness between two randomly moving particles in a fractured medium

This paper presents the stronger moment conditions which are sufficient to show the finiteness of the first collision time between N-dimensional Gaussian jump particle and another N-dimensional Brownian particle in a fractured medium. To obtain these conditions, we use the triangular arrays of the random sequence vector which gives all probable positions of the first collision at any time. This study is an extension of the analytical study which is detailed in Alzulaibani and El-Hadidy [Int. J. Mod. Phys. B 33(28) (2019) 1950334] using the uniform integrability conditions.