Browse > Article
http://dx.doi.org/10.4134/BKMS.2015.52.2.483

MULTIDIMENSIONAL BSDES WITH UNIFORMLY CONTINUOUS GENERATORS AND GENERAL TIME INTERVALS  

Fan, Shengjun (College of Sciences China University of Mining and Technology, School of Mathematical Sciences Fudan University)
Wang, Yanbin (College of Sciences China University of Mining and Technology)
Xiao, Lishun (College of Sciences China University of Mining and Technology)
Publication Information
Bulletin of the Korean Mathematical Society / v.52, no.2, 2015 , pp. 483-504 More about this Journal
Abstract
This paper is devoted to solving a multidimensional backward stochastic differential equation with a general time interval, where the generator is uniformly continuous in (y, z) non-uniformly with respect to t. By establishing some results on deterministic backward differential equations with general time intervals, and by virtue of Girsanov's theorem and convolution technique, we prove a new existence and uniqueness result for solutions of this kind of backward stochastic differential equations, which extends the results of [8] and [6] to the general time interval case.
Keywords
backward stochastic differential equation; general time interval; existence and uniqueness; uniformly continuous generator;
Citations & Related Records
연도 인용수 순위
  • Reference
1 P. Briand, J.-P. Lepeltier, and J. San Martin, One-dimensional backward stochastic differential equations whose coefficient is monotonic in y and non-Lipschitz in z, Bernoulli 13 (2007), no. 1, 80-91.   DOI   ScienceOn
2 Z. Chen and B. Wang, Infinite time interval BSDEs and the convergence of g-martingales, J. Austral. Math. Soc. Ser. A 69 (2000), no. 2, 187-211.   DOI
3 N. El Karoui, S. Peng, and M. C. Quenez, Backward stochastic differential equations in finance, Math. Finance 7 (1997), no. 1, 1-71.   DOI   ScienceOn
4 S. Fan and L. Jiang, Finite and infinite time interval BSDEs with non-Lipschitz coefficients, Statist. Probab. Lett. 80 (2010), no. 11-12, 962-968.   DOI   ScienceOn
5 S. Fan, L. Jiang, and M. Davison, Uniqueness of solutions for multidimensional BSDEs with uniformly continuous generators, C. R. Math. Acad. Sci. Paris 348 (2010), no. 11-12, 683-686.   DOI   ScienceOn
6 S. Fan, L. Jiang, and D. Tian, One-dimensional BSDEs with finite and infinite time horizons, Stochastic Process. Appl. 121 (2011), no. 3, 427-440.   DOI   ScienceOn
7 S. Hamadene, Multidimensional backward stochastic differential equations with uniformly continuous coefficients, Bernoulli 9 (2003), no. 3, 517-534.   DOI   ScienceOn
8 M. Kobylanski, Backward stochastic differential equations and partial differential equations with quadratic growth, Ann. Probab. 28 (2000), no. 2, 558-602.   DOI   ScienceOn
9 J.-P. Lepeltier and J. San Martin, Backward stochastic differential equations with continuous coefficient, Statist. Probab. Lett. 32 (1997), no. 4, 425-430.   DOI   ScienceOn
10 X. Mao, Adapted solutions of backward stochastic differential equations with non-Lipschitz coefficients, Stochastic Process. Appl. 58 (1995), no. 2, 281-292.   DOI   ScienceOn
11 E. Pardoux and S. Peng, Adapted solution of a backward stochastic differential equation, Systems Control Lett. 14 (1990), no. 1, 55-61.   DOI   ScienceOn
12 Y. Wang and Z. Huang, Backward stochastic differential equations with non-Lipschitz coefficients, Statist. Probab. Lett. 79 (2009), no. 12, 1438-1443.   DOI   ScienceOn
13 K. Bahlali, Backward stochastic differential equations with locally Lipschitz coefficient, C. R. Math. Acad. Sci. Paris 333 (2001), no. 5 481-486.   DOI   ScienceOn