Comparison theorems for stochastic differential inequalities and an application to reaction–diffusion equations with random sources
Catherine Bandle, Marco Dozzi · Stochastic Analysis and Applications · 1994
Comparison theorems for stochastic differential inequalities of ordinary and parabolic type are derived. Two methods are proposed, one exploiting the diffentiability of the solutions at the starting time and one based on Gronwall's inequality. The results are then applied to reaction–diffusion processes with random sources. Emphasis is put on the question whether or not those sources have an influence on t he blow up of the solutions