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

Bonaccorsi Stefano; Zanella Margherita

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

机译：带有边界噪声的随机微分方程解的密度的存在性和正则性

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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.

机译：我们研究了具有布朗运动和分数布朗运动随机扰动的非线性热扩散解的密度的存在性和正则性：我们使用Malliavin微积分来证明，如果非线性项是适当正则的，则定律为该溶液相对于Lebesgue测度具有平滑的密度。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2016年第1期|共24页
作者
Bonaccorsi Stefano; Zanella Margherita;
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正文语种 eng
中图分类物理学;
关键词
Density of the solution; fractional Brownian motion; stochastic boundary condition;

机译：解的密度;分数布朗运动;随机边界条件;

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专利

1. Existence and regularity of the density for solutions of stochastic differential equations with boundary noise [J] . Bonaccorsi Stefano, Zanella Margherita Infinite dimensional analysis, quantum probability, and related topics . 2016,第1期

机译：带有边界噪声的随机微分方程解的密度的存在性和正则性
2. EXISTENCE CRITERIA FOR SOLUTIONS OF LINEAR STOCHASTIC DIFFERENTIAL EQUATIONS WITH SKEW-SYMMETRIC DIFFERENTIAL OPERATOR AND ADDITIVE FRACTIONAL BROWNIAN NOISE [J] . BORIS P. BELINSKIY, PETER CAITHAMER Stochastics and dynamics . 2009,第1期

机译：偏对称微分算子和偏对称微分算子的线性随机微分方程解的存在性准则
3. Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Levy noise [J] . Albeverioa S, Mandrekar V, Rudiger B Stochastic Processes and Their Applications: An Official Journal of the Bernoulli Society for Mathematical Statistics and Probability . 2009,第3期

机译：具有非高斯利维噪声的随机微分方程和半线性方程组的温和解的存在性
4. Existence and regularity of weak solutions for the Navier-Stokes equations with partial sli p boundary conditions [C] . Juergen Saal Kyoto Conference on the Navier-Stokes Equations and their Applications . 2007

机译：具有部分SLI P边界条件的Navier-Stokes方程弱解决方案的存在与规律
5. Applications of the Gaussian stochastic analysis of fractional Brownian noise to regularity of stochastic heat equations and to portfolio optimization. [D] . Sarol, Yalcin. 2005

机译：分数布朗噪声的高斯随机分析在随机热方程的规律性和投资组合优化中的应用。
6. Existence and Uniqueness of Solution for a Class of Stochastic Differential Equations [O] . Junfei Cao, Zaitang Huang, Caibin Zeng 2013

机译：一类随机微分方程解的存在唯一性
7. Existence and Regularity of the Density for Solutions to Stochastic Differential Equations with Boundary Conditions [O] . Arturo Kohatsu-higa, Marta Sanz-Sole 2007

机译：具边界条件的随机微分方程解的密度存在性与正则性

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

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