Dirichlet Heat Kernel Estimates for Subordinate Brownian Motions with Gaussian Components

2013/03/26 by Zhen-Qing Chen, Chen, Zhen-Qing, Panki Kim +3
Economics, Econometrics and Finance · Mathematics · #47G20 #60J75 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Primary 60J35 #Probability (math.PR) #Secondary 47D07 #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1303.6626

openalex publication_date 2013/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we derive explicit sharp two-sided estimates for the Dirichlet heat kernels, in C^1,1 open sets D in R^d, of a large class of subordinate Brownian motions with Gaussian components. When D is bounded, our sharp two-sided Dirichlet heat kernel estimates hold for all t>0. Integrating the heat kernel estimates with respect to the time variable t, we obtain sharp two-sided estimates for the Green functions, in bounded C^1,1 open sets, of such subordinate Brownian motions with Gaussian components.

Citations

• Two-sided eigenvalue estimates for subordinate processes in domains

Related

• Estimates of Dirichlet heat kernels for subordinate Brownian motions
• Heat kernel estimates for subordinate Brownian motions
• Dirichlet heat kernel estimates of subordinate diffusion processes with diffusive components in C^{1, α} open sets
• Global Heat Kernel Estimates for Δ+Δ^α/2 in Half-space-like domains
• Heat Kernel Estimate for Δ+Δ^α/2 in C^1,1 open sets