• Corpus ID: 250089281

Parabolic Anderson model on Heisenberg groups: the It\^o setting

@inproceedings{Baudoin2022ParabolicAM,
  title={Parabolic Anderson model on Heisenberg groups: the It\^o setting},
  author={Fabrice Baudoin and Cheng Ouyang and Samy Tindel and Jing Wang},
  year={2022}
}
In this note we focus our attention on a stochastic heat equation defined on the Heisenberg group H of order n. This equation is written as ∂tu = 12∆u+ uẆα, where ∆ is the hypoelliptic Laplacian on H and {Ẇα;α > 0} is a family of Gaussian space-time noises which are white in time and have a covariance structure generated by (−∆)−α in space. Our aim is threefold: (i) Give a proper description of the noise Wα; (ii) Prove that one can solve the stochastic heat equation in the Itô sense as soon as… 

References

SHOWING 1-10 OF 37 REFERENCES

Stochastic heat equation driven by fractional noise and local time

The aim of this paper is to study the d-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and has the covariance of a fractional Brownian motion with

Moment asymptotics for parabolic Anderson equation with fractional time-space noise: In Skorokhod regime

. In this paper, we consider the parabolic Anderson equation that is driven by a Gaussian noise fractional in time and white or fractional in space, and is solved in a mild sense defined by Skorokhod

The Parabolic Anderson Model: Random Walk in Random Potential

This is a comprehensive survey on the research on the parabolic Anderson model the heat equation with random potential or the random walk in random potential of the years 1990 2015. The investigation

Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency

This paper studies the stochastic heat equation with multiplicative noises of the form uW, where W is a mean zero Gaussian noise and the differential element uW is interpreted both in the sense of

Quenched asymptotics for Brownian motion in generalized Gaussian potential

In this paper, we study the long-term asymptotics for the quenched moment \[\mathbb{E}_x\exp \biggl\{\int_0^tV(B_s)\,ds\biggr\}\] consisting of a $d$-dimensional Brownian motion $\{B_s;s\ge 0\}$ and

Radial processes for sub-Riemannian Brownian motions and applications

We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. It\^o's formula is proved for the radial processes associated to Riemannian distances

Fractional Gaussian fields: A survey

We discuss a family of random fields indexed by a parameter s ∈ R which we call the fractional Gaussian fields, given by FGFs(R) = (−∆)−s/2W, where W is a white noise on Rd and (−∆)−s/2 is the

Analysis Of Stochastic Partial Differential Equations

The general area of stochastic PDEs is interesting to mathematicians because it contains an enormous number of challenging open problems. There is also a great deal of interest in this topic because