We study the deterministic characteristics of stochastic processes through investigation of random walks and the heat equation. The relationship is confirmed by discretizing the heat equation in time and space and determining the probability distribution function for random walks in dimension d = 1, 2. The existence of the relationship is presented both through theoretical analysis and numerical computation.
Makker, Gurmehar Singh, "Determinism of Stochastic Processes through the Relationship between the Heat Equation and Random Walks" (2019). CUNY Academic Works.