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Markov selections and Feller properties of nonlinear diffusions

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  • Criens, David
  • Niemann, Lars

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.

Suggested Citation

  • Criens, David & Niemann, Lars, 2024. "Markov selections and Feller properties of nonlinear diffusions," Stochastic Processes and their Applications, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:spapps:v:173:y:2024:i:c:s0304414924000607
    DOI: 10.1016/j.spa.2024.104354
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    References listed on IDEAS

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