Global Heat Kernel Estimate for Relativistic Stable Processes in Exterior Open Sets

2011/12/13 by Zhen-Qing Chen, Chen, Zhen-Qing, Panki Kim +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #47G20 #60J35 #60J75 #Cosmology and Gravitation Theories #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1112.2778

openalex publication_date 2011/12/13 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper, sharp two-sided estimates for the transition densities of relativistic α-stable processes with mass m∈ (0, 1] in C^1,1 exterior open sets are established for all time t>0. These transition densities are also the Dirichlet heat kernels of m-(m^2/α-Δ)^α/2 with m∈ (0, 1] in C^1,1 exterior open sets. The estimates are uniform in m in the sense that the constants are independent of m∈ (0, 1]. As a corollary of our main result, we establish sharp two-sided Green function estimates for relativistic α-stable processes with mass m∈ (0, 1] in C^1,1 exterior open sets.

Related

• Two-sided estimates for the transition densities of symmetric Markov processes dominated by stable-like processes in C^1,η open sets
• Global heat kernel estimates for symmetric Markov processes dominated by stable-like processes in exterior C^1,η open sets
• Heat Kernel Estimate for Δ+Δ^α/2 in C^1,1 open sets
• Global Heat Kernel Estimates for Fractional Laplacians in Unbounded Open Sets
• Spectral heat content for α-stable processes in C1,1 open sets