On the Analytical Solution with Existence of Reduced First Collision Time Between a Brownian and Gaussian Jump Particles in the Interactive Medium.

AbstractIn this paper, we provide some analytical results about the finiteness of the reduced first collision time between a Brownian and Gaussian jump particles in the interactive medium. These results depend on the influence of discounted effort-reward parameter on the jumping distance. More than using the effectiveness of this parameter on uniform integrability conditions, we study the behavior of the triangular arrays of the random sequence with this discount parameter that represents the probable positions of the first collision at any time t∈R+. This will give more stronger finite moment conditions which are sufficient for the existence of finiteness of this reducing time. [ABSTRACT FROM AUTHOR]