# Stability of solutions of BSDEs with random terminal time

ESAIM: Probability and Statistics (2006)

- Volume: 10, page 141-163
- ISSN: 1292-8100

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topToldo, Sandrine. "Stability of solutions of BSDEs with random terminal time." ESAIM: Probability and Statistics 10 (2006): 141-163. <http://eudml.org/doc/249626>.

@article{Toldo2006,

abstract = {
In this paper, we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely
finite random terminal time. More precisely, we are going to show that if (Wn) is a sequence of scaled random walks or a sequence of
martingales that converges to a Brownian motion W and if $(\tau^n)$ is a sequence of stopping times that converges to a stopping time
τ, then the solution of the BSDE driven by Wn with random terminal time $\tau^n$ converges to the solution of the BSDE driven by
W with random terminal time τ.
},

author = {Toldo, Sandrine},

journal = {ESAIM: Probability and Statistics},

keywords = {Backward Stochastic Differential Equations (BSDE); stability of BSDEs; weak convergence of filtrations; stopping times.; backward stochastic differential equations (BSDE); stability of bsdes; stopping times},

language = {eng},

month = {3},

pages = {141-163},

publisher = {EDP Sciences},

title = {Stability of solutions of BSDEs with random terminal time},

url = {http://eudml.org/doc/249626},

volume = {10},

year = {2006},

}

TY - JOUR

AU - Toldo, Sandrine

TI - Stability of solutions of BSDEs with random terminal time

JO - ESAIM: Probability and Statistics

DA - 2006/3//

PB - EDP Sciences

VL - 10

SP - 141

EP - 163

AB -
In this paper, we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely
finite random terminal time. More precisely, we are going to show that if (Wn) is a sequence of scaled random walks or a sequence of
martingales that converges to a Brownian motion W and if $(\tau^n)$ is a sequence of stopping times that converges to a stopping time
τ, then the solution of the BSDE driven by Wn with random terminal time $\tau^n$ converges to the solution of the BSDE driven by
W with random terminal time τ.

LA - eng

KW - Backward Stochastic Differential Equations (BSDE); stability of BSDEs; weak convergence of filtrations; stopping times.; backward stochastic differential equations (BSDE); stability of bsdes; stopping times

UR - http://eudml.org/doc/249626

ER -

## References

top- F. Antonelli and A. Kohatsu-Higa, Filtration stability of backward SDE's. Stochastic Anal. Appl.18 (2000) 11–37. Zbl0953.60044
- P. Billingsley, Convergence of Probability Measures, Second Edition. Wiley and Sons, New York (1999). Zbl0944.60003
- P. Briand, B. Delyon and J. Mémin, Donsker-type theorem for BSDEs. Electron. Comm. Probab.6 (2001) 1–14 (electronic). Zbl0977.60067
- P. Briand, B. Delyon and J. Mémin, On the robustness of backward stochastic differential equations. Stochastic Process. Appl.97 (2002) 229–253. Zbl1058.60041
- K.L. Chung and Z.X. Zhao, From Brownian motion to Schrödinger's equation, Springer-Verlag, Berlin Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 312 (1995). Zbl0819.60068
- F. Coquet, V. Mackevičius and J. Mémin, Stability in D of martingales and backward equations under discretization of filtration. Stochastic Process. Appl.75 (1998) 235–248. Zbl0932.60047
- F. Coquet, V. Mackevičius and J. Mémin, Corrigendum to: “Stability in D of martingales and backward equations under discretization of filtration”. Stochastic Process. Appl.82 (1999) 335–338. Zbl0997.60061
- F. Coquet, J. Mémin and L. Słomiński, On weak convergence of filtrations. Séminaire de probabilités XXXV, Springer-Verlag, Berlin Heidelberg New York, Lect. Notes Math.1755 (2001) 306–328. Zbl0987.60009
- J. Haezendonck and F. Delbaen, Caractérisation de la tribu des événements antérieurs à un temps d'arrêt pour un processus stochastique. Acad. Roy. Belg., Bulletin de la Classe Scientifique56 (1970) 1085–1092. Zbl0232.60032
- D.N. Hoover, Convergence in distribution and Skorokhod convergence for the general theory of processes. Probab. Theory Related Fields89 (1991) 239–259. Zbl0725.60005
- J. Jacod and A.N. Shiryaev, Limit Theorems for Stochastic Processes, Springer-Verlag, Berlin Heidelberg New York (1987). Zbl0635.60021
- I. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, Second Edition. Springer-Verlag, Berlin Heidelberg New York (1991). Zbl0734.60060
- J. Ma, P. Protter, J. San Martín and S. Torres, Numerical method for backward stochastic differential equations. Ann. Appl. Probab.12 (2002) 302–316. Zbl1017.60074
- S. Peng, Probabilistic interpretation for systems of quasilinear parabolic partial differential equations. Stoch. Stoch. Rep.37 (1991) 61–74. Zbl0739.60060
- M. Royer, BSDEs with a random terminal time driven by a monotone generator and their links with PDEs. Stoch. Stoch. Rep.76 (2004) 281–307. Zbl1055.60062

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