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Blow-up estimates for a system of semilinear SPDEs driven by mixed fractional Brownian motions (2207.12343v2)
Published 25 Jul 2022 in math.PR and math.AP
Abstract: In this paper, we obtain the existence and finite-time blow-up for the solution to a system of semilinear stochastic partial differential equations driven by a combination of Brownian and fractional Brownian motions. Under suitable assumptions, lower and upper bounds for the finite-time blow-up solution are obtained. We provide sufficient conditions for the existence of a global weak solution to the system. Further, a lower bound for the probability of the finite-time blow-up solution of the considered system is provided by using Malliavin calculus.