A class of multidimensional nonlinear diffusions with the Feller property

被引：1

作者：

Criens, David ^{[1
]}

Niemann, Lars ^{[1
]}

机构：

[1] Albert Ludwigs Univ Freiburg, Ernst Zermelo Str, D-79104 Freiburg, Germany

来源：

STATISTICS & PROBABILITY LETTERS | 2024年 / 208卷

关键词：

Nonlinear Markov processes; Sublinear semigroup; Nonlinear expectation; Partial differential equation; Viscosity solution; Knightian uncertainty; G-BROWNIAN MOTION; STOCHASTIC CALCULUS;

D O I：

10.1016/j.spl.2024.110057

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页数：6

共 48 条

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