Dirichlet heat kernel for unimodal Lévy processes
نویسندگان
چکیده
منابع مشابه
Dirichlet Heat Kernel Estimates for Rotationally Symmetric Lévy processes
In this paper, we consider a large class of purely discontinuous rotationally symmetric Lévy processes. We establish sharp two-sided estimates for the transition densities of such processes killed upon leaving an open set D. When D is a κ-fat open set, the sharp two-sided estimates are given in terms of surviving probabilities and the global transition density of the Lévy process. When D is a C...
متن کاملHeat Kernel Estimates for Dirichlet Fractional Laplacian
In this paper, we consider the fractional Laplacian −(−∆)α/2 on an open subset in R with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such Dirichlet fractional Laplacian in C open sets. This heat kernel is also the transition density of a rotationally symmetric α-stable process killed upon leaving a C open set. Our results are the first sharp two-sided ...
متن کاملDirichlet Heat Kernel Estimates for Δ +δ
For d ≥ 1 and 0 < β < α < 2, consider a family of pseudo differential operators {Δ + aΔ; a ∈ [0,1]} on R that evolves continuously from Δ to Δ + Δ. It gives arise to a family of Lévy processes {X, a ∈ [0,1]} on R, where each X is the independent sum of a symmetric α-stable process and a symmetric β-stable process with weight a. For any C open set D ⊂R, we establish explicit sharp two-sided esti...
متن کاملDirichlet heat kernel estimates for stable processes with singular drift in unbounded C open sets
Suppose d ≥ 2 and α ∈ (1, 2). Let D be a (not necessarily bounded) C open set in R and μ = (μ, . . . , μ) where each μ is a signed measure on R belonging to a certain Kato class of the rotationally symmetric α-stable process X. Let X be an α-stable process with drift μ in R and let X be the subprocess of X in D. In this paper, we derive sharp two-sided estimates for the transition density of X....
متن کاملDirichlet Heat Kernel Estimates for Fractional Laplacian with Gradient Perturbation
By Zhen-Qing Chen∗,‡, Panki Kim†,§ and Renming Song¶ University of Washington‡, Seoul National University§ and University of Illinois¶ Suppose that d ≥ 2 and α ∈ (1, 2). Let D be a bounded C open set in R and b an R-valued function on R whose components are in a certain Kato class of the rotationally symmetric α-stable process. In this paper, we derive sharp two-sided heat kernel estimates for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2014
ISSN: 0304-4149
DOI: 10.1016/j.spa.2014.06.001