
Previous Article
The Cauchy problem of Backward Stochastic SuperParabolic Equations with Quadratic Growth
 PUQR Home
 This Issue

Next Article
Affine processes under parameter uncertainty
Law of large numbers and central limit theorem under nonlinear expectations
Institute of Mathematics, Shandong University, Jinan 250100, Shandong Province, China 
References:
[1] 
Cabre, X. and Caffarelli, L.A. (1997). Fully nonlinear elliptic partial differential equations, American Mathematical Society., 
[2] 
Caffarelli, L.A. (1989). Interior estimates for fully nonlinear equations, Ann. of Math. 130, 189213., 
[3] 
Peng, S. (2004). Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims, Acta Mathematicae Applicatae Sinica, Engl. Ser. 20, no. 2, 124., 
[4] 
Peng, S. (2005). Nonlinear expectations and nonlinear Markov chains, Chin. Ann. Math. 26B, no. 2, 159184., 
[5] 
Peng, S. (2007). GExpectation, GBrownian Motion and Related Stochastic Calculus of Itô's type. in Stochastic Analysis and Applications, The Abel Symposium 2005, Abel Symposia2, Edit. Benth et. al., 541567, SpringerVerlag., 
[6] 
Peng, S. (2008). MultiDimensional GBrownian Motion and Related Stochastic Calculus under GExpectation. Stochastic Processes and their Applications 118(12), 22232253., 
[7] 
Wang, L. (1992). On the regularity of fully nonlinear parabolic equations:II, Comm. Pure Appl. Math. 45, 141178., 
show all references
References:
[1] 
Cabre, X. and Caffarelli, L.A. (1997). Fully nonlinear elliptic partial differential equations, American Mathematical Society., 
[2] 
Caffarelli, L.A. (1989). Interior estimates for fully nonlinear equations, Ann. of Math. 130, 189213., 
[3] 
Peng, S. (2004). Filtration Consistent Nonlinear Expectations and Evaluations of Contingent Claims, Acta Mathematicae Applicatae Sinica, Engl. Ser. 20, no. 2, 124., 
[4] 
Peng, S. (2005). Nonlinear expectations and nonlinear Markov chains, Chin. Ann. Math. 26B, no. 2, 159184., 
[5] 
Peng, S. (2007). GExpectation, GBrownian Motion and Related Stochastic Calculus of Itô's type. in Stochastic Analysis and Applications, The Abel Symposium 2005, Abel Symposia2, Edit. Benth et. al., 541567, SpringerVerlag., 
[6] 
Peng, S. (2008). MultiDimensional GBrownian Motion and Related Stochastic Calculus under GExpectation. Stochastic Processes and their Applications 118(12), 22232253., 
[7] 
Wang, L. (1992). On the regularity of fully nonlinear parabolic equations:II, Comm. Pure Appl. Math. 45, 141178., 
[1] 
Peng Luo. Comparison theorem for diagonally quadratic BSDEs. Discrete & Continuous Dynamical Systems  A, 2020 doi: 10.3934/dcds.2020374 
[2] 
Vivina Barutello, Gian Marco Canneori, Susanna Terracini. Minimal collision arcs asymptotic to central configurations. Discrete & Continuous Dynamical Systems  A, 2021, 41 (1) : 6186. doi: 10.3934/dcds.2020218 
[3] 
Fabio Camilli, Giulia Cavagnari, Raul De Maio, Benedetto Piccoli. Superposition principle and schemes for measure differential equations. Kinetic & Related Models, , () : . doi: 10.3934/krm.2020050 
[4] 
Harrison Bray. Ergodicity of Bowen–Margulis measure for the Benoist 3manifolds. Journal of Modern Dynamics, 2020, 16: 305329. doi: 10.3934/jmd.2020011 
[5] 
Mark F. Demers. Uniqueness and exponential mixing for the measure of maximal entropy for piecewise hyperbolic maps. Discrete & Continuous Dynamical Systems  A, 2021, 41 (1) : 217256. doi: 10.3934/dcds.2020217 
[6] 
Gunther Uhlmann, Jian Zhai. Inverse problems for nonlinear hyperbolic equations. Discrete & Continuous Dynamical Systems  A, 2021, 41 (1) : 455469. doi: 10.3934/dcds.2020380 
[7] 
Predrag S. Stanimirović, Branislav Ivanov, Haifeng Ma, Dijana Mosić. A survey of gradient methods for solving nonlinear optimization. Electronic Research Archive, 2020, 28 (4) : 15731624. doi: 10.3934/era.2020115 
[8] 
Thomas Bartsch, Tian Xu. Strongly localized semiclassical states for nonlinear Dirac equations. Discrete & Continuous Dynamical Systems  A, 2021, 41 (1) : 2960. doi: 10.3934/dcds.2020297 
[9] 
Hua Chen, Yawei Wei. Multiple solutions for nonlinear cone degenerate elliptic equations. Communications on Pure & Applied Analysis, , () : . doi: 10.3934/cpaa.2020272 
[10] 
Abdelghafour Atlas, Mostafa Bendahmane, Fahd Karami, Driss Meskine, Omar Oubbih. A nonlinear fractional reactiondiffusion system applied to image denoising and decomposition. Discrete & Continuous Dynamical Systems  B, 2020 doi: 10.3934/dcdsb.2020321 
[11] 
Xuefei He, Kun Wang, Liwei Xu. Efficient finite difference methods for the nonlinear Helmholtz equation in Kerr medium. Electronic Research Archive, 2020, 28 (4) : 15031528. doi: 10.3934/era.2020079 
[12] 
Thierry Cazenave, Ivan Naumkin. Local smooth solutions of the nonlinear Kleingordon equation. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020448 
[13] 
Zhiyan Ding, Qin Li, Jianfeng Lu. Ensemble Kalman Inversion for nonlinear problems: Weights, consistency, and variance bounds. Foundations of Data Science, 2020 doi: 10.3934/fods.2020018 
[14] 
Yuxia Guo, Shaolong Peng. A direct method of moving planes for fully nonlinear nonlocal operators and applications. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020462 
[15] 
Scipio Cuccagna, Masaya Maeda. A survey on asymptotic stability of ground states of nonlinear Schrödinger equations II. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020450 
[16] 
Kihoon Seong. Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2020, 19 (12) : 54375473. doi: 10.3934/cpaa.2020247 
[17] 
José Luis López. A quantum approach to KellerSegel dynamics via a dissipative nonlinear Schrödinger equation. Discrete & Continuous Dynamical Systems  A, 2020 doi: 10.3934/dcds.2020376 
[18] 
Maoding Zhen, Binlin Zhang, Vicenţiu D. Rădulescu. Normalized solutions for nonlinear coupled fractional systems: Low and high perturbations in the attractive case. Discrete & Continuous Dynamical Systems  A, 2020 doi: 10.3934/dcds.2020379 
[19] 
Zedong Yang, Guotao Wang, Ravi P. Agarwal, Haiyong Xu. Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator. Discrete & Continuous Dynamical Systems  S, 2020 doi: 10.3934/dcdss.2020436 
[20] 
Claudianor O. Alves, Rodrigo C. M. Nemer, Sergio H. Monari Soares. The use of the Morse theory to estimate the number of nontrivial solutions of a nonlinear Schrödinger equation with a magnetic field. Communications on Pure & Applied Analysis, , () : . doi: 10.3934/cpaa.2020276 
Impact Factor:
Tools
Metrics
Other articles
by authors
[Back to Top]