Forward-Invariance and Wong-Zakai Approximation for Stochastic Moving Boundary Problems
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Date
2018-01-16Type
- Working Paper
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Abstract
We discuss a class of stochastic second-order PDEs in one space-dimension with an inner boundary moving according to a possibly non-linear, Stefan-type condition. We show that proper separation of phases is attained, i.e., the solution remains negative on one side and positive on the other side of the moving interface, when started with the appropriate initial conditions. To extend results from deterministic settings to the stochastic case, we establish a Wong-Zakai type approximation. After a coordinate transformation the problems are reformulated and analysed in terms of stochastic evolution equations on domains of fractional powers of linear operators. Show more
Publication status
publishedExternal links
Journal / series
arXivPages / Article No.
Publisher
Cornell UniversitySubject
Stochastic partial differential equation; Stefan problem; Moving boundary problem; Phase separation; Forward invariance; Wong-Zakai approximationOrganisational unit
09546 - Larsson, Martin (ehemalig) / Larsson, Martin (former)
Funding
163425 - Tractable Stopping Problems in Finance (SNF)
Related publications and datasets
Is previous version of: http://hdl.handle.net/20.500.11850/379255
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ETH Bibliography
yes
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