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Existence and space-time regularity for stochastic heat equations on p.c.f. fractals

Abstract:

We define linear stochastic heat equations (SHE) on p.c.f.s.s. sets equipped with regular harmonic structures. We show that if the spectral dimension of the set is less than two, then function-valued “random-field” solutions to these SPDEs exist and are jointly Hölder continuous in space and time. We calculate the respective Hölder exponents, which extend the well-known results on the Hölder exponents of the solution to SHE on the unit interval. This shows that the “curse of dimensionality” ...

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Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1214/18-EJP148

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
St Annes College
ORCID:
0000-0003-0086-0695
More by this author
Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Engineering and Physical Sciences Research Council More from this funder
Publisher:
Institute of Mathematical Statistics Publisher's website
Journal:
Electronic Journal of Probability Journal website
Volume:
23
Pages:
Article: 22
Publication date:
2018-02-27
Acceptance date:
2018-02-06
DOI:
EISSN:
1083-6489
Pubs id:
pubs:823075
URN:
uri:e1af8f3b-2611-480f-bce1-5dfeb63a83dc
UUID:
uuid:e1af8f3b-2611-480f-bce1-5dfeb63a83dc
Local pid:
pubs:823075

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