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Backward stochastic differential equations with Young drift
Convergence to a selfnormalized GBrownian motion
School of Mathematical Sciences, Zhejiang University, Hangzhou 310027 China 
References:
[1] 
Csörgö, M, Szyszkowicz, B, Wang, QY:Donsker's theorem for selfnormalized partial sums processes. Ann. Probab 31, 12281240 (2003) 
[2] 
Denis, L, Hu, MS, Peng, SG:Function spaces and capacity related to a sublinear expectation:application to GBrownian Motion Paths. Potential Anal 34, 139161 (2011). arXiv:0802.1240v1[math.PR] 
[3] 
Giné, E, Götze, F, Mason, DM:When is the Student tstatistic asymptotically standard normal? Ann.Probab 25, 15141531 (1997) 
[4] 
Hu, MS, Ji, SL, Peng, SG, Song, YS:Backward stochastic differential equations driven by GBrownian motion. Stochastic Process. Appl 124(1), 759784 (2014a) 
[5] 
Hu, MS, Ji, SL, Peng, SG, Song, YS:Comparison theorem, FeynmanKac formula and Girsanov transformation for BSDEs driven by GBrownian motion. Stochastic Process. Appl 124(2), 11701195(2014b) 
[6] 
Li, XP, Peng, SG:Topping times and related Ito's calculus with GBrownian motion. Stochastic Process.Appl 121(7), 14921508 (2011) 
[7] 
Nutz, M, van Handel, R:Constructing sublinear expectations on path space. Stochastic Process. Appl 123(8), 31003121 (2013) 
[8] 
Peng, SG:Gexpectation, GBrownian motion and related stochastic calculus of Ito's type. The Abel Symposium 2005, Abel Symposia 2, Edit. Benth et. al, pp. 541567. SpringerVerlag (2006) 
[9] 
Peng, SG:Multidimensional GBrownian motion and related stochastic calculus under Gexpectation.Stochastic Process. Appl 118(12), 22232253 (2008a) 
[10] 
Peng, SG:A new central limit theorem under sublinear expectations (2008b). Preprint:arXiv:0803.2656v1[math.PR] 
[11] 
Peng, SG:Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations. Sci. China Ser. A 52(7), 13911411 (2009) 
[12] 
Peng, SG:Nonlinear Expectations and Stochastic Calculus under Uncertainty (2010a). Preprint:arXiv:1002.4546[math.PR] 
[13] 
Peng, SG:Tightness, weak compactness of nonlinear expectations and application to CLT (2010b).Preprint:arXiv:1006.2541[math.PR] 
[14] 
Yan, D, Hutz, M, Soner, HM:Weak approximation of Gexpectations. Stochastic Process. Appl 122(2), 664675 (2012) 
[15] 
Zhang, LX:Donsker's invariance principle under the sublinear expectation with an application to Chung's law of the iterated logarithm. Commun. Math. Stat 3(2), 187214 (2015). arXiv:1503.02845[math.PR] 
[16] 
Zhang, LX:Rosenthal's inequalities for independent and negatively dependent random variables under sublinear expectations with applications. Sci. China Math 59(4), 751768 (2016) 
show all references
References:
[1] 
Csörgö, M, Szyszkowicz, B, Wang, QY:Donsker's theorem for selfnormalized partial sums processes. Ann. Probab 31, 12281240 (2003) 
[2] 
Denis, L, Hu, MS, Peng, SG:Function spaces and capacity related to a sublinear expectation:application to GBrownian Motion Paths. Potential Anal 34, 139161 (2011). arXiv:0802.1240v1[math.PR] 
[3] 
Giné, E, Götze, F, Mason, DM:When is the Student tstatistic asymptotically standard normal? Ann.Probab 25, 15141531 (1997) 
[4] 
Hu, MS, Ji, SL, Peng, SG, Song, YS:Backward stochastic differential equations driven by GBrownian motion. Stochastic Process. Appl 124(1), 759784 (2014a) 
[5] 
Hu, MS, Ji, SL, Peng, SG, Song, YS:Comparison theorem, FeynmanKac formula and Girsanov transformation for BSDEs driven by GBrownian motion. Stochastic Process. Appl 124(2), 11701195(2014b) 
[6] 
Li, XP, Peng, SG:Topping times and related Ito's calculus with GBrownian motion. Stochastic Process.Appl 121(7), 14921508 (2011) 
[7] 
Nutz, M, van Handel, R:Constructing sublinear expectations on path space. Stochastic Process. Appl 123(8), 31003121 (2013) 
[8] 
Peng, SG:Gexpectation, GBrownian motion and related stochastic calculus of Ito's type. The Abel Symposium 2005, Abel Symposia 2, Edit. Benth et. al, pp. 541567. SpringerVerlag (2006) 
[9] 
Peng, SG:Multidimensional GBrownian motion and related stochastic calculus under Gexpectation.Stochastic Process. Appl 118(12), 22232253 (2008a) 
[10] 
Peng, SG:A new central limit theorem under sublinear expectations (2008b). Preprint:arXiv:0803.2656v1[math.PR] 
[11] 
Peng, SG:Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations. Sci. China Ser. A 52(7), 13911411 (2009) 
[12] 
Peng, SG:Nonlinear Expectations and Stochastic Calculus under Uncertainty (2010a). Preprint:arXiv:1002.4546[math.PR] 
[13] 
Peng, SG:Tightness, weak compactness of nonlinear expectations and application to CLT (2010b).Preprint:arXiv:1006.2541[math.PR] 
[14] 
Yan, D, Hutz, M, Soner, HM:Weak approximation of Gexpectations. Stochastic Process. Appl 122(2), 664675 (2012) 
[15] 
Zhang, LX:Donsker's invariance principle under the sublinear expectation with an application to Chung's law of the iterated logarithm. Commun. Math. Stat 3(2), 187214 (2015). arXiv:1503.02845[math.PR] 
[16] 
Zhang, LX:Rosenthal's inequalities for independent and negatively dependent random variables under sublinear expectations with applications. Sci. China Math 59(4), 751768 (2016) 
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