Analytic Properties of Markov Semigroup Generated by Stochastic Differential Equations Driven by L,vy Processes

被引：1

作者：

Fernando, Pani W. ^{[1
]}

Hausenblas, Erika ^{[1
]}

Razafimandimby, Paul ^{[1
]}

机构：

[1] Univ Leoben, Lehrstuhl Angew Math, Franz Josef Str E 18, A-8700 Leoben, Austria

来源：

POTENTIAL ANALYSIS | 2017年 / 46卷 / 01期

基金：

奥地利科学基金会;

关键词：

Hoh's symbol; Markovian semigroup; Pseudo-differential operator L'evy process; Generalized Blumenthal-Getoor index; Sobolev-Slobodeckii spaces;

D O I：

10.1007/s11118-016-9570-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the stochastic differential equation (SDE) of the form where is globally Lipschitz continuous and L={L(t):ta0} is a L,vy process. Under this condition on sigma it is well known that the above problem has a unique solution X. Let be the Markovian semigroup associated to X defined by , ta0, , . Let B be a pseudo-differential operator characterized by its symbol q. Fix . In this article we investigate under which conditions on sigma, L and q there exist two constants gamma > 0 and C > 0 such that vertical bar BPtu vertical bar H-2(rho) <= C t(-gamma) vertical bar u vertical bar H-2(rho), (sic)u is an element of H-2(rho) (R-d), t > 0.

引用

页码：1 / 21

页数：21