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A stochastic representation theorem for sublinear semigroups with non-local generators (2311.03138v2)
Published 6 Nov 2023 in math.PR and math.AP
Abstract: In this paper we investigate sublinear semigroups whose pointwise generators are given by non-local Hamilton-Jacobi-BeLLMan operators. Our main result provides a stochastic representation in terms of a family of sublinear (conditional) expectations that can be understood as a nonlinear Markov family with uncertain local characteristics. The proofs are based on viscosity methods.