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Invariant measures for stochastic heat equations with unbounded coefficients
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Assing, Sigurd and Manthey, Ralf (2003) Invariant measures for stochastic heat equations with unbounded coefficients. Stochastic Processes and their Applications, 103 (2). 237 - 256.
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Official URL: http://dx.doi.org/10.1016/S0304-4149(02)00211-9
Abstract
The paper deals with the Cauchy problem in Rd of a stochastic heat equation ∂u/∂t=λΔu+f(u)+σ(u)Ẇ. The locally lipschitz drift coefficient f can have polynomial growth while the diffusion coefficient σ is supposed to be lipschitz but not necessarily bounded. Of course, for the existence of a solution alone, a certain dissipativity of f is needed. Applying the comparison method, a condition on the strength of this dissipativity is derived even ensuring the existence of an invariant measure.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
| Journal or Publication Title: | Stochastic Processes and their Applications | ||||||
| Publisher: | Elsevier Science BV | ||||||
| ISSN: | 0304-4149 | ||||||
| Official Date: | 2 February 2003 | ||||||
| Dates: |
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| Volume: | 103 | ||||||
| Number: | 2 | ||||||
| Page Range: | 237 - 256 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published |
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