Survey on normal distributions, central limit theorem, Brownian motion and the related stochastic calculus under sublinear expectations

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Peng S. G-expectation, G-Brownian motion and related stochastic calculus of Itô’s type. In: Stochastic Analysis and Applications, The Abel Symposium 2005, Abel Symposia · 2. New York: Springer-Verlag, 2006, 541–567

Peng S. Law of large numbers and central limit theorem under nonlinear expectations. arXiv:math.PR/07-02358v1 13 Feb 2007

Peng S. G-Brownian motion and dynamic risk measure under volatility uncertainty. arXiv:0711.2834v1 [math.PR] 19 Nov 2007

Peng S. Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation. Stochastic Processes Appl, 118(12):2223–2253 (2008)

Peng S. A new central limit theorem under sublinear expectations. arXiv:0803.2656v1 [math.PR] 18 Mar 2008

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Denis L, Martini C. A theoretical framework for the pricing of contingent claims in the presence of model uncertainty. Ann Appl Probab, 16(2): 827–852 (2006)

Denis L, Hu M, Peng S. Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion pathes. arXiv:0802.1240v1 [math.PR] 9 Feb, 2008

Hu M. Explicit solutions of G-heat equation with a class of initial conditions by G-Brownian motion. Submitted paper, 2008

Hu M, Peng S. On representation theorem of G-expectations and paths of G-Brownian motion. Acta Math Appl Sinica English Series, 25(3): 1–8 (2009)

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Lin Q. Stochastic differential equations driven by G-Brownian motion. Preprint, 2008

Xu J, Zhang B. Martingale characterization of G-Brownian motion. Stochastic Processes Appl, 119(1): 232–248 (2009)

Liao M. G-Browian motion in Lie groups, Preprint, 2009

Peng S. Filtration consistent nonlinear expectations and evaluations of contingent claims. Acta Math Appl Sin Engl Ser, 20(2): 1–24 (2004)

Peng S. Nonlinear expectations and nonlinear Markov chains. Chinese Ann Math Ser B, 26(2): 159–184 (2005)

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Peng S. Backward SDE and related g-expectation. In: Backward Stochastic Differential Equations, Pitman Research Notes in Math. Series, No. 364. El Karoui Mazliak ed. Boca Raton: Chapman & Hall/CRC, 1997, 141–159

Coquet F, Hu Y, Memin J, et al. Filtration-consistent nonlinear expectations and related g-expectations. Probab Theory Related Fields, 123: 1–27 (2002)

Peng S. Monotonic limit theorem of BSDE and nonlinear decomposition theorem of Doob-Meyer’s type. Probab Theory Related Fields, 113(4): 473–499 (1999)

Rosazza Gianin E. Some examples of risk measures via g-expectations. Insurance Math Econom, 39: 19–34 (2006)

Barrieu P, El Karoui N. Pricing, hedging and optimally designing derivatives via minimization of risk measures. To appear in: Volume on Indifference Pricing. Princeton: Princeton University, 2009

Delbaen F, Rosazza Gianin E, Peng S. m-Stable sets, risk measures and g-expectations. Preprint, 2005