Stochastic heat equation with rough dependence in space

Yaozhong Hu (1) , Jingyu Huang (1) , Khoa Lê (1) , David Nualart (1) , Samy Tindel (2, 3)

1 Department of Mathematics [Lawrence, Kansas]
2 BIGS - Biology, genetics and statistics
3 IECL - Institut Élie Cartan de Lorraine

This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter 1/4

Mots clés: Stochastic heat equation; Fractional Brownian motion; Feynman-Kac formula; Wiener chaos expansion; Intermittency

Domaines: Probabilités [math.PR]; Mathématiques générales [math.GM]

Yaozhong Hu, Jingyu Huang, Khoa Lê, David Nualart, Samy Tindel. Stochastic heat equation with rough dependence in space. 2015. ⟨hal-01153045⟩