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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

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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:
DateEvent
2 February 2003Published
1 September 2002Accepted
Volume: 103
Number: 2
Page Range: 237 - 256
Status: Peer Reviewed
Publication Status: Published

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