Parabolic Anderson model with rough noise in space and rough initial conditions

2022/06/22 by Raluca M. Balan, Le Chen, Balan, Raluca M. +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2206.11361

openalex publication_date 2022/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we consider the parabolic Anderson model on ℝ₊ × ℝ, driven by a Gaussian noise which is fractional in time with index H₀>1/2 and fractional in space with index 03/4. Under a general condition on the initial data, we prove the existence and uniqueness of the mild solution and obtain its exponential upper bounds in time for all p-th moments with p≥ 2.

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