Forward-Invariance and Wong-Zakai Approximation for Stochastic Moving Boundary Problems
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2018-01-16
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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.
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published
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1801.05203
Publisher
Cornell University
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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)
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Funding
163425 - Tractable Stopping Problems in Finance (SNF)
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