Markov selections and Feller properties of nonlinear diffusions

David Criens and Lars Niemann

Stochastic Processes and their Applications, 2024, vol. 173, issue C

Abstract: In this paper we study a family of nonlinear (conditional) expectations that can be understood as a diffusion with uncertain local characteristics. Here, the differential characteristics are prescribed by a set-valued function. We establish its Feller properties and examine how to linearize the associated sublinear Markovian semigroup. In particular, we observe a novel smoothing effect of sublinear semigroups in frameworks which carry enough randomness. Furthermore, we link the value function corresponding to the semigroup to a nonlinear Kolmogorov equation. This provides a connection to the so-called Nisio semigroup.

Keywords: Nonlinear diffusion; Nonlinear semimartingales; Nonlinear Markov processes; Sublinear expectation; Sublinear semigroup; Nonlinear expectation; Partial differential equation; Viscosity solution; Semimartingale characteristics; Knightian uncertainty (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104354

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