# Positive random walks and an identity for half-space SPDEs

@article{Parekh2022PositiveRW, title={Positive random walks and an identity for half-space SPDEs}, author={Shalin Parekh}, journal={Electronic Journal of Probability}, year={2022} }

The purpose of this article is threefold. First, we introduce a new type of boundary condition for the multiplicative-noise stochastic heat equation on the half space. This is essentially a Dirichlet boundary condition but with a nontrivial normalization near the boundary which leads to inhomogeneous transition densities (roughly, those of a Brownian \textit{meander}) within the associated chaos series. Secondly, we prove a new convergence result of the directed-polymer partition function in an…

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## 12 Citations

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