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Teoriya Veroyatnostei i ee Primeneniya, 2005, Volume 50, Issue 2, Pages 390–396
DOI: https://doi.org/10.4213/tvp117 (Mi tvp117) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Short Communications

A backward stochastic differential equation without strong solution

R. Buckdahna, H. J. Engelbertb

a Université de Bretagne Occidentale
b Friedrich-Schiller-University
Full-text PDF (840 kB) Citations (10)
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DOI: https://doi.org/10.4213/tvp117
Abstract: 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.
Received: 05.06.2004
English version:
Theory of Probability and its Applications, 2006, Volume 50, Issue 2, Pages 284–289
DOI: https://doi.org/10.1137S0040585X97981743
Bibliographic databases:
Document Type: Article
Language: English
Citation: R. Buckdahn, H. J. Engelbert, “A backward stochastic differential equation without strong solution”, Teor. Veroyatnost. i Primenen., 50:2 (2005), 390–396; Theory Probab. Appl., 50:2 (2006), 284–289
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tvp/v50/i2/p390
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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