Research Communication | Open Access
Volume 2021 | Communication ID 160
Volume 2021 | Communication ID 160
| Local time for stochastic heat equation |
Yassine Nachit
Received |
Accepted |
Published |
January 30, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: We consider the solution to a system of d non-linear stochastic heat equations in spatial dimension one driven by d-dimensional space-time white noise. We prove that the local time of the non-linear stochastic heat equation exists when d ≤ 3 and it does not exist when d ≥ 4. We also show joint continuity for the local time of the non-linear stochastic heat equation, and establish Holder conditions of the local time. These results are then used to investigate the irregularity of the coordinate functions of the non-linear stochastic heat equation. Based on similar results in the case of ...