Representation theorems for generators of backward stochastic differential equations

Long Jiang

doi:10.1016/j.crma.2004.10.023

Probability Theory

Representation theorems for generators of backward stochastic differential equations
[Théorèmes de représentation pour générateurs d'équations différentielles stochastiques rétrogrades]

Présenté par : Paul Malliavin

Long Jiang ^1,²

¹ Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, China
² School of Mathematics and System Sciences, Shandong University, Jinan 250100, China

Comptes Rendus. Mathématique, Volume 340 (2005) no. 2, pp. 161-166.

Résumé
Abstract

Dans cette Note on montre que le générateur g d'une équation stochastique rétrograde (EDSR) peut être représentré par la solution de l'EDSR correspondante si et seulement si g est un générateur de Lebesgue.

It is proved that the generator g of a backward stochastic differential equation (BSDE) can be represented by the solutions of the corresponding BSDEs if and only if g is a Lebesgue generator.

Reçu le : 2004-06-17
Accepté le : 2004-09-19
Publié le : 2005-01-05

DOI : 10.1016/j.crma.2004.10.023

Affiliations des auteurs :

Long Jiang ^{1, 2}

¹ Department of Mathematics, China University of Mining and Technology, Xuzhou 221008, China
² School of Mathematics and System Sciences, Shandong University, Jinan 250100, China

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     title = {Representation theorems for generators of backward stochastic differential equations},
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Long Jiang. Representation theorems for generators of backward stochastic differential equations. Comptes Rendus. Mathématique, Volume 340 (2005) no. 2, pp. 161-166. doi : 10.1016/j.crma.2004.10.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.10.023/

Bibliographie
Cité par

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Panyu Wu; Guodong Zhang Representation theorems for generators of BSDEs and the extended g-expectations in probability spaces with general filtration, Journal of Mathematical Analysis and Applications, Volume 487 (2020) no. 2, p. 124010 | DOI:10.1016/j.jmaa.2020.124010
Shi-qiu Zheng; Shou-mei Li Representation Theorem for Generators of Quadratic BSDEs, Acta Mathematicae Applicatae Sinica, English Series, Volume 34 (2018) no. 3, p. 622 | DOI:10.1007/s10255-018-0772-8
Shiqiu Zheng; Shoumei Li Representation theorems for generators of BSDEs with monotonic and convex growth generators, Statistics Probability Letters, Volume 97 (2015), p. 197 | DOI:10.1016/j.spl.2014.12.002
Kun He; Mingshang Hu Representation Theorem for Generators of BSDEs Driven by -Brownian Motion and Its Applications, Abstract and Applied Analysis, Volume 2013 (2013), p. 1 | DOI:10.1155/2013/342038
Li Song; Feng Hu; Zeng-jing Chen Representation theorems for generators of BSDEs in L p spaces, Acta Mathematicae Applicatae Sinica, English Series, Volume 28 (2012) no. 2, p. 255 | DOI:10.1007/s10255-012-0143-9
ShengJun Fan; Long Jiang; YingYing Xu Representation Theorem for Generators of BSDEs with Monotonic and Polynomial-Growth Generators in the Space of Processes, Electronic Journal of Probability, Volume 16 (2011) no. none | DOI:10.1214/ejp.v16-873
ShengJun Fan; Long Jiang A representation theorem for generators of BSDEs with continuous linear-growth generators in the space of processes, Journal of Computational and Applied Mathematics, Volume 235 (2010) no. 3, p. 686 | DOI:10.1016/j.cam.2010.06.022
Sheng-Jun Fan; Jian-Hua Hu A limit theorem for solutions to BSDEs in the space of processes, Statistics Probability Letters, Volume 78 (2008) no. 8, p. 1024 | DOI:10.1016/j.spl.2007.09.062
Sheng Jun Fan A Relationship Between the Conditional g-Evaluation System and the Generator g and Its Applications, Acta Mathematica Sinica, English Series, Volume 23 (2007) no. 8, p. 1427 | DOI:10.1007/s10114-007-0943-7

Cité par 9 documents. Sources : Crossref

^⁎ Supported by the National Natural Science Foundation of China (No. 10131030) and Science Foundation of CUMT.

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