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

[41] Viscosity solution theory of a class of nonlinear degenerate parabolic equations I. Uniqueness and existence of viscosity solutions
Zhan Y.
Acta Mathematicae Applicatae Sinica, 1997, 13 (2) : 136 - 144
[42] A strong minimum principle and large time asymptotics for viscosity solutions to a class of doubly nonlinear possibly degenerate parabolic equations
Bhattacharya, Tilak
Marazzi, Leonardo
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2022, 221
[43] Error estimates for a class of finite difference-quadrature schemes for fully nonlinear degenerate parabolic integro-PDEs
Biswas, Imran H.
Jakobsen, Espen R.
Karlsen, Kenneth H.
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2008, 5 (01) : 187 - 219
[44] On the sets of regularity of solutions for a class of degenerate nonlinear elliptic fourth-order equations with L1 data
Bonafede, S.
Nicolosi, F.
BOUNDARY VALUE PROBLEMS, 2007, 2007 (1)
[45] Nonlinear BSDEs with Two Optional Doob’s Class Barriers Satisfying Weak Mokobodzki’s Condition and Extended Dynkin Games
Tomasz Klimsiak
Maurycy Rzymowski
Applied Mathematics & Optimization, 2023, 88
[46] Nonlinear BSDEs with Two Optional Doob's Class Barriers Satisfying Weak Mokobodzki's Condition and Extended Dynkin Games
Klimsiak, Tomasz
Rzymowski, Maurycy
APPLIED MATHEMATICS AND OPTIMIZATION, 2023, 88 (03)
[47] Existence and Uniqueness of Periodic Solutions for a Class of Nonlinear Equations with [inline-graphic not available: see fulltext]-Laplacian-Like Operators
Hui-Sheng Ding
Guo-Rong Ye
Wei Long
Advances in Difference Equations, 2010
[48] On the Sets of Regularity of Solutions for a Class of Degenerate Nonlinear Elliptic Fourth-Order Equations with[inline-graphic not available: see fulltext] Data
S Bonafede
F Nicolosi
Boundary Value Problems, 2007

← 1 2 3 4 5 →