A bidirectional hitting probability for the symmetric Hunt processes

Yasuhito Nishimori

Statistics & Probability Letters, 2024, vol. 204, issue C

Abstract: We write σA the first hitting time of set A for the Hunt processes. Let B and BR be compact sets, where BR states far away from B. We assume that the Hunt process is irreducible and conservative and satisfies the Feller property. We consider a relation of the hitting probability of B from BR with the hitting probability of BR from B, without the spatial homogeneity. Our claim is that if the Hunt process satisfies the strong Feller property, then limx→∞Px(σB≤t)=0 implies that limR→∞Py(σBR≤t)=0, for y∈B. Additionally, if the Hunt process is m-symmetric, then both statements are equivalent.

Date: 2024
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DOI: 10.1016/j.spl.2023.109942

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