Mathematics > Probability
[Submitted on 3 Oct 2022 (v1), last revised 1 Oct 2024 (this version, v3)]
Title:Scaling limit of a long-range random walk in time-correlated random environment
View PDF HTML (experimental)Abstract:This paper concerns a long-range random walk in random environment in dimension $1+1$, where the environmental disorder is independent in space but has long-range correlations in time. We prove that two types of rescaled partition functions converge weakly to the Stratonovich solution and the Itô-Skorohod solution respectively of a fractional stochastic heat equation with multiplicative Gaussian noise which is white in space and colored in time.
Submission history
From: Jian Song [view email][v1] Mon, 3 Oct 2022 15:20:07 UTC (37 KB)
[v2] Thu, 1 Jun 2023 14:55:22 UTC (42 KB)
[v3] Tue, 1 Oct 2024 07:17:49 UTC (42 KB)
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