On estimates of the density of Feynman-Kac semigroups of α-stable-like processes

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:348

Article

Wang, Chunlin

关键词: alpha-stable-like processes;    nonsymmetric;    kato class;    Feynman-Kac semigroups;    discontinuous additive functionals;   

DOI  :  10.1016/j.jmaa.2008.02.012

来源: Elsevier

【 摘 要 】

Suppose that alpha is an element of (0, 2) and that X is an alpha-stable-like process on R-d. Let F be a function on R-d belonging to the class J(d, alpha) (see Introduction) and A(t)(F) be Sigma(s <= t) F(Xs-, X-s), t > 0, a discontinuous additive functional of X. With neither F nor X being symmetric, under certain conditions, we show that the Feynman-Kac semigroup {S-t(F) : t >= 0} defined by S-t(F) f(x) = E-x(e(-AtF) f(X-t)) has a density q and that there exist positive constants C-1, C-2, C-3 and C-4 such that C(1)e(-C2t)t(-d/alpha)(1 boolean AND t(1/alpha)/vertical bar x-y vertical bar)(d+alpha)<= q(t, x, y)<= C(3)e(C4t)t(-d/alpha)(1 boolean AND t(1/alpha)vertical bar x-y vertical bar)(d+alpha) for all (t, x, y) is an element of (0, infinity) x R-d x R-d. (C) 2008 Published by Elsevier Inc.

【 授权许可】

Free