# Forward invariance and Wong–Zakai approximation for stochastic moving boundary problems

@article{KellerRessel2019ForwardIA, title={Forward invariance and Wong–Zakai approximation for stochastic moving boundary problems}, author={Martin Keller-Ressel and Marvin S. Mueller}, journal={Journal of Evolution Equations}, year={2019} }

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…

## One Citation

Approximation of the interface condition for stochastic Stefan-type problems

- MathematicsDiscrete & Continuous Dynamical Systems - B
- 2019

We discuss approximations of the Stefan-type condition for semilinear stochastic moving boundary problems by local imbalances of volume inside of the system. Stochastic Stefan-type problems came up…

## References

SHOWING 1-10 OF 44 REFERENCES

A stochastic Stefan-type problem under first-order boundary conditions

- MathematicsThe Annals of Applied Probability
- 2018

Moving boundary problems allow to model systems with phase transition at an inner boundary. Driven by problems in economics and finance, in particular modeling of limit order books, we consider a…

A Stefan-type stochastic moving boundary problem

- Mathematics
- 2016

Motivated by applications in economics and finance, in particular to the modeling of limit order books, we study a class of stochastic second-order PDEs with non-linear Stefan-type boundary…

Approximation of the interface condition for stochastic Stefan-type problems

- MathematicsDiscrete & Continuous Dynamical Systems - B
- 2019

We discuss approximations of the Stefan-type condition for semilinear stochastic moving boundary problems by local imbalances of volume inside of the system. Stochastic Stefan-type problems came up…

Wong-Zakai approximations of stochastic evolution equations

- Mathematics
- 2006

Abstract.Theorems on weak convergence of the laws of the Wong-Zakai approximations for evolution equation
$$ \begin{aligned} dX(t) & = (AX(t) + F(X(t)))dt + G(X(t))dW(t)\\
X(0) & = x \in H…

Wong-Zakai approximations for stochastic differential equations

- Mathematics, Computer Science
- 1996

The author's results are preceded by the introduction of two new forms of correction terms in infinite dimensions appearing in the Wong-Zakai approximations, and these results are divided into four parts: for stochastic delay equations, for semilinear and nonlinear Stochastic equations in abstract spaces, and for the Navier-Stokes equations.

Viability Theorem for SPDE's Including HJM Framework

- Mathematics
- 2004

A viability theorem is proven for the mild solution of the stochastic differential equation in a Hilbert space of the form: � dX x (t )= AX x (t)dt + b(X x (t))dt + σ(X x (t))dB(t), X x (0) = x. It…

Continuous dependence on the coefficients and global existence for stochastic reaction diffusion equations

- Mathematics
- 2011

Analytic Semigroups and Optimal Regularity in Parabolic Problems

- Mathematics
- 2003

Introduction.- 0 Preliminary material: spaces of continuous and Holder continuous functions.- 1 Interpolation theory.- Analytic semigroups and intermediate spaces.- 3 Generation of analytic…

Geometric Theory of Semilinear Parabolic Equations

- Mathematics
- 1989

Preliminaries.- Examples of nonlinear parabolic equations in physical, biological and engineering problems.- Existence, uniqueness and continuous dependence.- Dynamical systems and liapunov…

ON THE RELATION BETWEEN ORDINARY AND STOCHASTIC DIFFERENTIAL EQUATIONS

- Mathematics, Computer Science
- 1965