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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 2, Pages 390–396 (Mi tvp117)  

This article is cited in 6 scientific papers (total in 6 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

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.

DOI: https://doi.org/10.4213/tvp117

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English version:
Theory of Probability and its Applications, 2006, 50:2, 284–289

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Received: 05.06.2004
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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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\by R.~Buckdahn, H.~J.~Engelbert
\paper A backward stochastic differential equation without strong solution
\jour Teor. Veroyatnost. i Primenen.
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\pages 390--396
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\transl
\jour Theory Probab. Appl.
\yr 2006
\vol 50
\issue 2
\pages 284--289
\crossref{https://doi.org/10.1137S0040585X97981743}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Theory Probab. Appl., 52:1 (2008), 152–160  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Yannacopoulos A.N., Frangos N.E., Karatzas I., “Wiener Chaos Solutions for Linear Backward Stochastic Evolution Equations”, SIAM J Math Anal, 43:1 (2011), 68–113  crossref  mathscinet  zmath  isi  scopus
    3. Ma J., Zhang J., “On weak solutions of forward-backward SDEs”, Probab Theory Related Fields, 151:3–4 (2011), 475–507  crossref  mathscinet  zmath  isi  scopus
    4. Bouchemella N., de Fitte P.R., “Weak Solutions of Backward Stochastic Differential Equations with Continuous Generator”, Stoch. Process. Their Appl., 124:1 (2014), 927–960  crossref  mathscinet  zmath  isi  scopus
    5. Carmona R., Delarue F., “Probabilistic Theory of Mean Field Games With Applications i: Mean Field Fbsdes, Control, and Games”, Probabilistic Theory of Mean Field Games With Applications i: Mean Field Fbsdes, Control, and Games, Probability Theory and Stochastic Modelling, 83, Springer International Publishing Ag, 2018, 1–713  crossref  mathscinet  zmath  isi
    6. Carmona R., Delarue F., “Probabilistic Theory of Mean Field Games With Applications II: Mean Field Games With Common Noise and Master Equations”, Probabilistic Theory of Mean Field Games With Applications II: Mean Field Games With Common Noise and Master Equations, Probability Theory and Stochastic Modelling, 84, Springer International Publishing Ag, 2018, 1–697  crossref  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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