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}
}
  • Shalin Parekh
  • Published 27 January 2019
  • Mathematics
  • Electronic Journal of Probability
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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