2024/10/17 by Torben Fattler, Fattler, Torben, Martin Grothaus +3
Economics, Econometrics and Finance · Mathematics · #60J55 #60J60 #FOS: Mathematics #Mathematical Dynamics and Fractals #Primary: 60J46 #Probability (math.PR) #Secondary: 60J65 #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2410.13814
openalex publication_date 2024/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The starting point is a gradient Dirichlet form with respect to \varrhoλd on the space L2(ℝd, \varrhoμ). Here λd is the Lebesgue measure on \mathbb Rd, \varrho a strictly positive density and μ puts weight on a set A⊂ \mathbb Rd with Lebesgue measure zero. We show that the Dirichlet form admits an associated stochastic process X. We derive an explicit representation of the corresponding generator if A is a Lipschitz boundary. This representation together with the Fukushima decomposition identifies X as a distorted Brownian motion with drift given by the logarithmic derivative of \varrho in \mathbb Rd ∖ A. Furthermore, we prove X to be irreducible and recurrent. Finally, via ergodicity we prove positive séjour time of X on A. Hence we obtain a stochastic process X with permeable sticky behaviour on A.