Stable process with singular drift

Panki Kim, Renming Song

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)2479-2516
Number of pages38
JournalStochastic Processes and their Applications
Issue number7
StatePublished - Jul 2014


  • 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


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