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LIAO Jun-xia, FAN Sheng-jun. Lp solutions of BSDEs with weakly monotonic and uniformly continuous generators[J]. Journal of East China Normal University (Natural Sciences), 2016, (6): 77-87. doi: 10.3969/j.issn.1000-5641.2016.06.008
Citation:
LIAO Jun-xia, FAN Sheng-jun. Lp solutions of BSDEs with weakly monotonic and uniformly continuous generators[J]. Journal of East China Normal University (Natural Sciences), 2016, (6): 77-87. doi: 10.3969/j.issn.1000-5641.2016.06.008
LIAO Jun-xia, FAN Sheng-jun. Lp solutions of BSDEs with weakly monotonic and uniformly continuous generators[J]. Journal of East China Normal University (Natural Sciences), 2016, (6): 77-87. doi: 10.3969/j.issn.1000-5641.2016.06.008
Citation:
LIAO Jun-xia, FAN Sheng-jun. Lp solutions of BSDEs with weakly monotonic and uniformly continuous generators[J]. Journal of East China Normal University (Natural Sciences), 2016, (6): 77-87. doi: 10.3969/j.issn.1000-5641.2016.06.008
This paper is devoted to solving one-dimensional backward stochastic differential equations (BSDEs) whose generator g satisfies a (p ^ 2)-order weak monotonicity condition together with a general growth condition in y and a uniform continuity condition in z. Using the convolution technique and Girsanovs theorem, we establish an existence and uniqueness result for Lp (p 1) solutions of this kind of BSDEs, which generalizes some existing results.
[ 1 ] PARDOUX E, PENG S G. Adaped solution of a backward stochastic differential equation[J]. Systems Control Letters, 1990, 14: 55-61.
[ 2 ] El KAROUI N, PENG S G, QUENEZM C. Backward stochastic differential equations in finance[J].Mathematical Finance, 1997, 7(1): 1-71.
[ 3 ] LEPELTIER J P, SAN MART´IN J. Backward stochastic differential equations with continuous coefficient[J]. Statistics and Probability Letters, 1997, 32: 425-430.
[ 4 ] BRIAND P, HU Y. BSDE with quadratic growth and unbounded terminal value[J]. Probability Theory and Related Fields, 2006, 136(4): 604-618.
[ 5 ] JIA G Y. A uniqueness theorem for the solution of backward stochastic differential equations[J]. Comptes Rendus Mathematigue, 2008, 346(7): 439-444.
[ 6 ] CHEN S K. Lp solutions of one-dimensional backward stochastic differential equations with continuous coefficients[J]. Stochastic Analysis and Applications, 2010, 28: 820-841.
[ 7 ] MA M, FAN S J, SONG X. Lp (p > 1) solutions of backward stochastic differential equations with monotonic and uniformly continuous generators[J]. Bulletin des Sciences Mathematiques, 2013, 137(2): 97-106.
[ 8 ] FAN S J. Lp solutions of multidimensional BSDEs with weak monotonicity and general growth generators[J]. Journal of Mathematical Analysis and Applications, 2015, 432: 156-178.
[ 9 ] FAN S J, JIANG L. BSDEs with uniformly continuous generators and integrable parameters [J]. Scientia Sinica Mathematica, 2012, 42(2): 119-131.
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