Two-sided estimates on the density of the feynman-kac semigroups of stable-like processes

Research output: Contribution to journalArticlepeer-review

Abstract

Suppose that α ∈ (0, 2) and that X is an α-stable-like process on Rd. Let μ be a signed measure on Rd belonging to the class Kd,α and Aμt be the continuous additive functional of X associated with μ. In this paper we show that the Feynman-Kac semigroup (Tμt : t ≥ 0) defined by Tμtf(x) = Ex(e−Aμt f(Xt)) has a density qμ and that there exist positive constants c1, c2, c3, c4 such that c1e−c2tt−d/α (1 ⋀ t1/α/|x − y|)d+α ≤ qμ(t, x, y) ≤ c3ec4tt−d/α (1 ⋀ t1/α/|x − y|)d+α for all (t, x, y) ∈ (0, ∞)×Rd×Rd. We also provide similar estimates for the densities of two other kinds of Feynman-Kac semigroups of X.

Original languageEnglish (US)
Pages (from-to)146-161
Number of pages16
JournalElectronic Journal of Probability
Volume11
DOIs
StatePublished - Jan 1 2006

Keywords

  • Continuous additive functionals
  • Continuous additive functionals of zero energy
  • Feynman-Kac semigroups
  • Kato class
  • Purely discontinuous additive functionals
  • Stable processes
  • Stable-like processes

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint

Dive into the research topics of 'Two-sided estimates on the density of the feynman-kac semigroups of stable-like processes'. Together they form a unique fingerprint.

Cite this