Backward doubly stochastic differential equations with infinite time horizon

Bo Zhu; Baoyan Han

Applications of Mathematics (2012)

  • Volume: 57, Issue: 6, page 641-653
  • ISSN: 0862-7940

Abstract

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We give a sufficient condition on the coefficients of a class of infinite horizon backward doubly stochastic differential equations (BDSDES), under which the infinite horizon BDSDES have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations.

How to cite

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Zhu, Bo, and Han, Baoyan. "Backward doubly stochastic differential equations with infinite time horizon." Applications of Mathematics 57.6 (2012): 641-653. <http://eudml.org/doc/247016>.

@article{Zhu2012,
abstract = {We give a sufficient condition on the coefficients of a class of infinite horizon backward doubly stochastic differential equations (BDSDES), under which the infinite horizon BDSDES have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations.},
author = {Zhu, Bo, Han, Baoyan},
journal = {Applications of Mathematics},
keywords = {infinite horizon; filtration; backward stochastic integral; backward doubly stochastic differential equations; infinite time horizon; backward doubly stochastic differential equations; filtration; backward stochastic integral},
language = {eng},
number = {6},
pages = {641-653},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Backward doubly stochastic differential equations with infinite time horizon},
url = {http://eudml.org/doc/247016},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Zhu, Bo
AU - Han, Baoyan
TI - Backward doubly stochastic differential equations with infinite time horizon
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 6
SP - 641
EP - 653
AB - We give a sufficient condition on the coefficients of a class of infinite horizon backward doubly stochastic differential equations (BDSDES), under which the infinite horizon BDSDES have a unique solution for any given square integrable terminal values. We also show continuous dependence theorem and convergence theorem for this kind of equations.
LA - eng
KW - infinite horizon; filtration; backward stochastic integral; backward doubly stochastic differential equations; infinite time horizon; backward doubly stochastic differential equations; filtration; backward stochastic integral
UR - http://eudml.org/doc/247016
ER -

References

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  1. Bally, V., Matoussi, A., 10.1023/A:1007825232513, J. Theor. Probab. 14 (2001), 125-164. (2001) MR1822898DOI10.1023/A:1007825232513
  2. Buckdahn, R., Ma, J., 10.1016/S0304-4149(00)00093-4, Stoch. Proc. Appl. 93 (2001), 181-204. (2001) Zbl1053.60065MR1828772DOI10.1016/S0304-4149(00)00093-4
  3. Buckdahn, R., Ma, J., 10.1016/S0304-4149(00)00092-2, Stoch. Proc. Appl. 93 (2001), 205-228. (2001) Zbl1053.60066MR1831830DOI10.1016/S0304-4149(00)00092-2
  4. Chen, Z., Wang, B., 10.1017/S1446788700002172, J. Aust. Math. Soc., Ser. A 69 (2000), 187-211. (2000) MR1775178DOI10.1017/S1446788700002172
  5. Darling, R., Pardoux, E., 10.1214/aop/1024404508, Ann. Probab. 25 (1997), 1135-1159. (1997) MR1457614DOI10.1214/aop/1024404508
  6. Karoui, N. El, Peng, S., Quenez, M. C., 10.1111/1467-9965.00022, Math. Finance 7 (1977), 1-71. (1977) MR1434407DOI10.1111/1467-9965.00022
  7. Ma, J., Protter, P., Yong, J., 10.1007/BF01192258, Theory Related Fields 98 (1994), 339-359. (1994) Zbl0794.60056MR1262970DOI10.1007/BF01192258
  8. Nualart, D., Pardoux, E., 10.1007/BF00353876, Probab. Theory Relat. Fields 78 (1988), 535-581. (1988) Zbl0629.60061MR0950346DOI10.1007/BF00353876
  9. Pardoux, E., Peng, S., 10.1016/0167-6911(90)90082-6, Syst. Control Lett. 14 (1990), 55-61. (1990) Zbl0692.93064MR1037747DOI10.1016/0167-6911(90)90082-6
  10. Pardoux, E., Peng, S., 10.1007/BF01192514, Probab. Theory Relat. Fields 98 (1994), 209-227. (1994) Zbl0792.60050MR1258986DOI10.1007/BF01192514
  11. Pardoux, E., Stochastic partial differential equations, Fudan Lecture Notes (2007). (2007) 
  12. Peng, S., 10.1080/17442509108833727, Stochastics Stochastics Rep. 37 (1991), 61-74. (1991) Zbl0739.60060MR1149116DOI10.1080/17442509108833727
  13. Peng, S., Backward Stochastic Differential Equations and Related g -expectation, Longman Harlow (1997), 141-159. (1997) MR1752680
  14. Peng, S., Shi, Y., 10.1016/S0304-4149(99)00066-6, Stoch. Proc. Appl. 85 (2000), 75-92. (2000) Zbl0997.60062MR1730617DOI10.1016/S0304-4149(99)00066-6
  15. Peng, S., Shi, Y., 10.1016/S1631-073X(03)00183-3, C. R. Math., Acad. Sci. Paris 336 (2003), 773-778. (2003) Zbl1031.60055MR1989279DOI10.1016/S1631-073X(03)00183-3
  16. Zhang, Q., Zhao, H., 10.1016/j.jfa.2007.06.019, J. Funct. Anal. 252 (2007), 171-219. (2007) Zbl1127.60059MR2357354DOI10.1016/j.jfa.2007.06.019
  17. Zhu, B., Han, B., 10.1155/2012/304781, J. Appl. Math. 2012 (Article ID 3047)81, doi:10.1155/2012/304781. Zbl1244.60064MR2910917DOI10.1155/2012/304781

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