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

[21] The cauchy problem for a class of nonlinear differential equations in a Banach space
Kuzenkov, OA
DIFFERENTIAL EQUATIONS, 2004, 40 (01) : 23 - 32
[22] The Cauchy Problem for a Class of Nonlinear Differential Equations in a Banach Space
O. A. Kuzenkov
Differential Equations, 2004, 40 : 23 - 32
[23] On the Bari Basis Property of the Eigenfunction System of a Nonlinear Integro-Differential Equation
P. E. Zhidkov
Differential Equations, 2002, 38 : 1260 - 1267
[24] On the Bari basis property of the eigenfunction system of a nonlinear integro-differential equation
Zhidkov, PE
DIFFERENTIAL EQUATIONS, 2002, 38 (09) : 1260 - 1267
[25] On the construction of maximal stable bridges in a class of nonlinear differential encounter games
Kamzolkin, DV
DIFFERENTIAL EQUATIONS, 2006, 42 (03) : 359 - 368
[26] On the construction of maximal stable bridges in a class of nonlinear differential encounter games
D. V. Kamzolkin
Differential Equations, 2006, 42 : 359 - 368
[27] Existence and multiplicity of weak solutions for a class of degenerate nonlinear elliptic equations
Mihai Mihăilescu
Boundary Value Problems, 2006
[28] Existence Result for a Class of Nonlinear Elliptic Systems on Punctured Unbounded Domains
Fabrice Colin
Boundary Value Problems, 2010
[29] A Class of Nonlinear Random Walks Related to the Ornstein-Uhlenbeck Process
Muzychka, S. A.
Vaninsky, K. L.
MARKOV PROCESSES AND RELATED FIELDS, 2011, 17 (02) : 277 - 304
[30] A note on the upper perturbation property and removable sets for fully nonlinear degenerate elliptic PDE
Andrzej Święch
Nonlinear Differential Equations and Applications NoDEA, 2019, 26

← 1 2 3 4 5 →