Abstract
Suppose that d≤2 and αε(1,2). Let μ=( μ1, ⋯, μd) be such that each μi is a signed measure on Rd belonging to the Kato class Kd,α-1. In this paper, we consider the stochastic differential equation dx t=dSt+dAt, where St is a symmetric α-stable process on Rd and for each j=1,⋯,d, the jth component Atj of At is a continuous additive functional of finite variation with respect to X whose Revuz measure is μj. The unique solution for the above stochastic differential equation is called an α-stable process with drift μ. We prove the existence and uniqueness, in the weak sense, of such an α-stable process with drift μ and establish sharp two-sided heat kernel estimates for such a process.
Original language | English (US) |
---|---|
Pages (from-to) | 2479-2516 |
Number of pages | 38 |
Journal | Stochastic Processes and their Applications |
Volume | 124 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2014 |
Keywords
- Boundary Harnack inequality
- Exit time
- Gradient operator
- Green function
- Heat kernel
- Kato class
- Lévy system
- Symmetric α-stable process
- Transition density
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics