On properties of a flow generated by an SDE with discontinuous drift

被引：4

作者：

Aryasova, Olga V. ^{[1
]}

Pilipenko, Andrey Yu. ^{[2
]}

机构：

[1] Natl Acad Sci Ukraine, Inst Geophys, Kiev, Ukraine

[2] Natl Acad Sci Ukraine, Inst Math, Kiev, Ukraine

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2012年 / 17卷

关键词：

stochastic flow; local times; differentiability with respect to initial data;

D O I：

10.1214/EJP.v17-2138

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider a stochastic flow on R generated by an SDE with its drift being a function of bounded variation. We show that the flow is differentiable with respect to the initial conditions. Asymptotic properties of the flow are studied.

引用

页码：1 / 20

页数：20

共 19 条

[1]

[Anonymous], CONTINUOUS MARTINGAL

[2] STOCHASTIC FLOWS OF DIFFEOMORPHISMS FOR ONE-DIMENSIONAL SDE WITH DISCONTINUOUS DRIFT [J].

Attanasio, Stefano .

ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2010, 15 :213-226

[3]

Barlow M, 2001, LECT NOTES MATH, V1755, P202

[4]

Billingsley P., 1968, CONVERGE PROBAB MEAS

[5]

Bouleau N., 1991, DEGRUYTER STUDIES MA

[6] Lenses in skew Brownian flow [J].

Burdzy, K ;

Kaspi, H .

ANNALS OF PROBABILITY, 2004, 32 (04) :3085-3115

[7] Flow of diffeomorphisms for SDEs with unbounded Holder continuous drift [J].

Flandoli, F. ;

Gubinelli, M. ;

Priola, E. .

BULLETIN DES SCIENCES MATHEMATIQUES, 2010, 134 (04) :405-422

[8] REAL VARIABLE LEMMA AND CONTINUITY OF PATHS OF SOME GAUSSIAN PROCESSES [J].

GARSIA, AM ;

RODEMICH, E ;

RUMSEY, H .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1970, 20 (06) :565-&

[9]

Gikhman II., 1968, STOCHASTIC DIFFERENT

[10]

Ikeda N., 1981, Stochastic Differential Equations and Diffusion Processes

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