A backward stochastic differential equation without strong solution
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 2, pp. 390-396
Voir la notice de l'article provenant de la source Math-Net.Ru
In [R. Buckdahn, H.-J. Engelbert, and A. Răşcanu, Theory Probab. Appl., 49 (2005), pp. 16–50] the notion of a weak solution of a general backward stochastic differential equation (BSDE) was introduced. There was also given an example of a weak solution for a certain BSDE which is not a strong solution, i.e., not a solution in the classical sense. However, the solution of the BSDE which was considered is not unique in law and, as was pointed out, there exist also strong solutions of this BSDE. In the present paper, we will remove this insufficiency and give an example of a BSDE which has a weak solution but does not possess any strong solution.
Keywords:
backward stochastic differential equations, weak solutions, strong solutions, Tsirelson example.
@article{TVP_2005_50_2_a13,
author = {R. Buckdahn and H. J. Engelbert},
title = {A backward stochastic differential equation without strong solution},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {390--396},
publisher = {mathdoc},
volume = {50},
number = {2},
year = {2005},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_2005_50_2_a13/}
}
TY - JOUR AU - R. Buckdahn AU - H. J. Engelbert TI - A backward stochastic differential equation without strong solution JO - Teoriâ veroâtnostej i ee primeneniâ PY - 2005 SP - 390 EP - 396 VL - 50 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_2005_50_2_a13/ LA - en ID - TVP_2005_50_2_a13 ER -
R. Buckdahn; H. J. Engelbert. A backward stochastic differential equation without strong solution. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 2, pp. 390-396. http://geodesic.mathdoc.fr/item/TVP_2005_50_2_a13/