Forward invariance and Wong-Zakai approximation for stochastic moving boundary problems
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Date
2020-09
Publication Type
Journal Article
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yes
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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 nonlinear, 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 analyzed in terms of stochastic evolution equations on domains of fractional powers of linear operators.
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published
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Journal / series
Volume
20 (3)
Pages / Article No.
869 - 929
Publisher
Springer
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Date collected
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Subject
Stochastic partial differential equation; Stefan problem; moving boundary problem; Phase separation; Forward invariance; Wong-Zakai approximation
Organisational unit
09546 - Larsson, Martin (ehemalig) / Larsson, Martin (former)
Notes
It was possible to publish this article open access thanks to a Swiss National Licence with the publisher.
Funding
163425 - Tractable Stopping Problems in Finance (SNF)
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