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2022 Parabolic Anderson model with rough noise in space and rough initial conditions
Raluca Balan, Le Chen, Yiping Ma
Author Affiliations +
Electron. Commun. Probab. 27: 1-12 (2022). DOI: 10.1214/22-ECP506


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>12 and fractional in space with index 0<H<12 such that H0+H>34. 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 p2.

Funding Statement

Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada (R. Balan) and partially by the Travel Support for Mathematicians from Simons Foundation (L. Chen).


The authors thank the anonymous referee for the careful reading and valuable comments.


Download Citation

Raluca Balan. Le Chen. Yiping Ma. "Parabolic Anderson model with rough noise in space and rough initial conditions." Electron. Commun. Probab. 27 1 - 12, 2022.


Received: 23 June 2022; Accepted: 11 December 2022; Published: 2022
First available in Project Euclid: 20 December 2022

MathSciNet: MR4529633
zbMATH: 1506.60061
Digital Object Identifier: 10.1214/22-ECP506

Primary: 60H15
Secondary: 60H07

Keywords: Dirac delta initial condition , Malliavin calculus , Parabolic Anderson model , Rough Gaussian noise , rough initial condition , Stochastic partial differential equations

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