On spider diffusions having a spinning measure selected from their own local time

2025/02/04 by Isaac Ohavi, Ohavi, Isaac, Miguel Martínez +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Mathematics #History and Theory of Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2502.02754

openalex publication_date 2025/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this article is to give several results related to Walsh's spider diffusions living on a star-shaped network that have a spinning measure selected from the own local time of the motion at the vertex (cf.[17]). We prove the corresponding Itô's formula and give some global trajectory properties such as L¹-approximation of the local time and the Markov property. Regarding the behavior of the process at the vertex, we show that that the distribution of the process is non atomic at the junction point and we characterize the instantaneous scattering distribution along some ray with the aid of the probability coefficients of diffraction. We obtain also a Feynmann-Kac representation for linear parabolic systems posed on star-shaped networks that where introduced in [18] possessing a so-called local-time Kirchhoff's boundary condition.

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