Existence and regularity of the density for solutions of stochastic differential equations with boundary noise

被引：4

作者：

Bonaccorsi, Stefano ^{[1
]}

Zanella, Margherita ^{[2
]}

机构：

[1] Univ Trent, Dipartimento Matemat, Via Sommarive 14, I-38123 Trento, Italy

[2] Univ Pavia, Dipartimento Matemat, Via Ferrata 1, I-27100 Pavia, Italy

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2016年 / 19卷 / 01期

关键词：

Density of the solution; fractional Brownian motion; stochastic boundary condition; DRIVEN; SPDE;

D O I：

10.1142/S0219025716500077

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the existence and regularity of densities for the solution of a nonlinear heat diffusion with stochastic perturbation of Brownian and fractional Brownian motion type: we use the Malliavin calculus in order to prove that, if the nonlinear term is suitably regular, then the law of the solution has a smooth density with respect to the Lebesgue measure.

引用

页数：24

共 50 条

[1] Existence and upper bound for the density of solutions of stochastic differential equations driven by generalized grey noise
da Silva, Jose Luis
Erraoui, Mohamed
STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC REPORTS, 2017, 89 (6-7): : 1116 - 1126
[2] On the Existence of Solutions with Smooth Density of Stochastic Differential Equations in Plane
周先银
Acta Mathematica Sinica, 1992, (04) : 432 - 446
[3] On the Existence of Solutions with Smooth Density of Stochastic Differential Equations in Plane
周先银
Acta Mathematica Sinica,English Series, 1992, (04) : 432 - 446
[4] The existence and uniqueness of mild solutions to stochastic differential equations with Levy noise
Wang, Lasheng
ADVANCES IN DIFFERENCE EQUATIONS, 2017,
[5] Existence and uniqueness of solutions for perturbed stochastic differential equations with reflected boundary
Bahaj, Faiz
Hiderah, Kamal
MONTE CARLO METHODS AND APPLICATIONS, 2024, 30 (01): : 31 - 41
[6] Absolute continuity of the law for solutions of stochastic differential equations with boundary noise
Bonaccorsi, Stefano
Zanella, Margherita
STOCHASTICS AND DYNAMICS, 2017, 17 (06)
[7] Existence and regularity of solutions to nonlocal retarded differential equations
Dubey, Shruti A.
Bahuguna, Dhirendra
APPLIED MATHEMATICS AND COMPUTATION, 2009, 215 (07) : 2413 - 2424
[8] The existence and uniqueness of mild solutions to stochastic differential equations with Lévy noise
Lasheng Wang
Advances in Difference Equations, 2017
[9] EXISTENCE AND REGULARITY OF MILD SOLUTIONS TO FRACTIONAL STOCHASTIC EVOLUTION EQUATIONS
Zou, G. A.
Wang, B.
Zhou, Y.
MATHEMATICAL MODELLING OF NATURAL PHENOMENA, 2018, 13 (01)
[10] Existence of Density for Solutions of Mixed Stochastic Equations
Shalaiko, Taras
Shevchenko, Georgiy
STOCHASTIC AND INFINITE DIMENSIONAL ANALYSIS, 2016, : 281 - 300

← 1 2 3 4 5 →