Estimates of Dirichlet heat kernels for subordinate Brownian motions

2017/08/29 by Panki Kim, Kim, Panki, Ante Mimica +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #60J35 #60J50 #60J75 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1708.08606

openalex publication_date 2017/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we discuss estimates of transition densities of subordinate Brownian motions in open subsets of Euclidean space. When D is a C^1,1 domain, we establish sharp two-sided estimates for the transition densities of a large class of subordinate Brownian motions in D whose scaling order is not necessarily strictly below 2. Our estimates are explicit and written in terms of the dimension, the Euclidean distance between two points, the distance to the boundary and Laplace exponent of the corresponding subordinator only.

Citations

• Boundary Harnack inequalities for regional fractional Laplacian
• On the boundary theory of subordinate killed Lévy processes

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