Wednesday, September 25, 2019 - 12:00 in X-E0-002
On the stochastic heat equation with sticky reflected boundary condition
A talk in the Keine Reihe series by
Martin Grothaus from TU Kaiserslautern
| Abstract: |
Via Dirichlet form techniques we constructed a Markov process corresponding to the gradient Dirichlet form with respect to the law of the modulus of the Brownian bridge.
The process is conjectured to be the scaling limit of the dynamical wetting model, also known as Ginzburg-Landau dynamics with pinning and reflection competing on the boundary.
In order to identify the constructed process as a solution of the stochastic heat equation with boundary condition, we prove an integration by parts formula for modulus of the Brownian bridge.
First we construct the generalized logarithmic derivative in the space of Hida distributions.
In a second step we identify the obtained distribution with a regular countable additive set function in a Gelfand triple.
This allows us to show that the constructed process is a solution to an infinite-dimensional Skorohod problem.
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