Integration by parts formula and applications to equations with jumps

被引：26

作者：

Bally, Vlad ^{[1
]}

Clement, Emmanuelle ^{[1
]}

机构：

[1] Univ Paris Est, Lab Anal & Math Appl, UMR 8050, F-77454 Marne La Vallee 2, France

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2011年 / 151卷 / 3-4期

关键词：

Integration by parts formula; Malliavin calculus; Stochastic equations; Poisson point measures; ABSOLUTE CONTINUITY; DENSITIES; EXISTENCE; CALCULUS;

D O I：

10.1007/s00440-010-0310-y

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 establish an integration by parts formula in an abstract framework in order to study the regularity of the law for processes arising as the solution of stochastic differential equations with jumps, including equations with discontinuous coefficients for which the Malliavin calculus developed by Bichteler et al. (Stochastics Monographs, vol 2. Gordon & Breach, New York, 1987) and Bismut (Z Wahrsch Verw Gebiete 63(2):147-235, 1983) fails.

引用

页码：613 / 657

页数：45

共 21 条

[1]

[Anonymous], ELECT J PROBAB

[2]

[Anonymous], 2004, STOCHASTICS STOCHAST, DOI 10.1080/10451120410001661250

[3]

Applebaum D., 2009, Commun. Stoch. Anal, V3, P119

[4]

Bally V., 2009, REGULARIZATION PROPE

[5] Integration by parts formula for locally smooth laws and applications to sensitivity computations [J].

Bally, Vlad ;

Bavouzet, Marie-Pierre ;

Messaoud, Marouen .

ANNALS OF APPLIED PROBABILITY, 2007, 17 (01) :33-66

[6] UNIQUENESS IN LAW FOR PURE JUMP MARKOV-PROCESSES [J].

BASS, RF .

PROBABILITY THEORY AND RELATED FIELDS, 1988, 79 (02) :271-287

[7] Computation of Greeks using Malliavin's calculus in jump type market models [J].

Bavouzet-Morel, MP ;

Messaoud, M .

ELECTRONIC JOURNAL OF PROBABILITY, 2006, 11 :276-300

[8]

Bichteler K., 1987, Stochastics Monographs, V2

[9]

Bismut J.-M., 1983, Z. Wahrscheinlichkeitstheor. Verw. Geb., V63, P147, DOI [10.1007/BF00538963, DOI 10.1007/BF00538963]

[10] Existence of densities for jumping stochastic differential equations [J].

Fournier, N ;

Giet, JS .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2006, 116 (04) :643-661

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