Analysis of the density of the solution to a semilinear SPDE with fractional noise

作者：Liu, Junfeng; Tudor, Ciprian A.^*

来源：Stochastics: An International Journal of Probability and Stochastic Processes , 2016, 88(7): 959-979.

DOI：10.1080/17442508.2016.1177056

• Stochastic partial differential equations
• fractional noise
• Malliavin calculus
• Gaussian density estimates
• smoothness of density
• 60G22
• 60H07
• 60H15

In this paper, we consider a general class of semilinear stochastic partial differential equations driven by a two-parameter fractional-coloured noise with Hurst index bigger than one half. Using the techniques of Malliavin calculus, we analyze the properties of the density of the solution. In particular, we establish lower and upper Gaussian-type bounds for the probability density of the mild solution at any fixed point and we prove the smoothness of this density.

• 出版日期2016
• 单位南京审计大学