Stability of solutions of BSDEs with random terminal time

Sandrine Toldo

ESAIM: Probability and Statistics (2006)

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

Abstract

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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 ( τ 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 τ n converges to the solution of the BSDE driven by W with random terminal time τ.

How to cite

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Toldo, 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

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