Stochastic heat equation with rough dependence in space

Yaozhong Hu ^[1] ; Jingyu Huang ^[1] ; Khoa Lê ^[1] ; David Nualart ^[1] ; Samy Tindel ^[2]
1. [1] University of Kansas
  
  University of Kansas
  
  City of Lawrence, Estados Unidos
2. [2] Purdue University
  
  Purdue University
  
  Township of Wabash, Estados Unidos
Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 45, Nº. 6, 2, 2017, págs. 4561-4616
Idioma: inglés
DOI: 10.1214/16-AOP1172
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Resumen
- 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 H∈(14,12)H∈(14,12) in the space variable. The existence and uniqueness of the solution uu are proved assuming the nonlinear coefficient σ(u)σ(u) is differentiable with a Lipschitz derivative and σ(0)=0σ(0)=0.