A class of multidimensional nonlinear diffusions with the Feller property

David Criens and Lars Niemann

Statistics & Probability Letters, 2024, vol. 208, issue C

Abstract: In this note we consider a family of nonlinear (conditional) expectations that can be understood as a multidimensional diffusion with uncertain drift and certain volatility. Here, the drift is prescribed by a set-valued function that depends on time and path in a Markovian way. We establish the Feller property for the associated sublinear Markovian semigroup and we observe a smoothing effect as our framework carries enough randomness. Furthermore, we link the corresponding value function to a semilinear Kolmogorov equation.

Keywords: Nonlinear Markov processes; Sublinear semigroup; Nonlinear expectation; Partial differential equation; Viscosity solution; Knightian uncertainty (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110057

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