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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 
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References:
[1] 
JeanPierre Conze, Stéphane Le Borgne, Mikaël Roger. Central limit theorem for stationary products of toral automorphisms. Discrete and Continuous Dynamical Systems, 2012, 32 (5) : 15971626. doi: 10.3934/dcds.2012.32.1597 
[2] 
James Nolen. A central limit theorem for pulled fronts in a random medium. Networks and Heterogeneous Media, 2011, 6 (2) : 167194. doi: 10.3934/nhm.2011.6.167 
[3] 
Oliver DíazEspinosa, Rafael de la Llave. Renormalization and central limit theorem for critical dynamical systems with weak external noise. Journal of Modern Dynamics, 2007, 1 (3) : 477543. doi: 10.3934/jmd.2007.1.477 
[4] 
Yves Derriennic. Some aspects of recent works on limit theorems in ergodic theory with special emphasis on the "central limit theorem''. Discrete and Continuous Dynamical Systems, 2006, 15 (1) : 143158. doi: 10.3934/dcds.2006.15.143 
[5] 
Xue Meng, Miaomiao Gao, Feng Hu. New proofs of Khinchin's law of large numbers and Lindeberg's central limit theorem –PDE's approach. Mathematical Foundations of Computing, 2022 doi: 10.3934/mfc.2022017 
[6] 
H.T. Banks, Jimena L. Davis. Quantifying uncertainty in the estimation of probability distributions. Mathematical Biosciences & Engineering, 2008, 5 (4) : 647667. doi: 10.3934/mbe.2008.5.647 
[7] 
Michael Björklund, Alexander Gorodnik. Central limit theorems in the geometry of numbers. Electronic Research Announcements, 2017, 24: 110122. doi: 10.3934/era.2017.24.012 
[8] 
Giuseppina di Blasio, Filomena Feo, Maria Rosaria Posteraro. Existence results for nonlinear elliptic equations related to Gauss measure in a limit case. Communications on Pure and Applied Analysis, 2008, 7 (6) : 14971506. doi: 10.3934/cpaa.2008.7.1497 
[9] 
David Simmons. Conditional measures and conditional expectation; Rohlin's Disintegration Theorem. Discrete and Continuous Dynamical Systems, 2012, 32 (7) : 25652582. doi: 10.3934/dcds.2012.32.2565 
[10] 
Benedetto Piccoli, Francesco Rossi. Measure dynamics with Probability Vector Fields and sources. Discrete and Continuous Dynamical Systems, 2019, 39 (11) : 62076230. doi: 10.3934/dcds.2019270 
[11] 
. Publisher Correction to: Probability, uncertainty and quantitative risk, volume 4. Probability, Uncertainty and Quantitative Risk, 2019, 4 (0) : 7. doi: 10.1186/s4154601900417 
[12] 
Simon Lloyd, Edson Vargas. Critical covering maps without absolutely continuous invariant probability measure. Discrete and Continuous Dynamical Systems, 2019, 39 (5) : 23932412. doi: 10.3934/dcds.2019101 
[13] 
Andrea Tosin, Paolo Frasca. Existence and approximation of probability measure solutions to models of collective behaviors. Networks and Heterogeneous Media, 2011, 6 (3) : 561596. doi: 10.3934/nhm.2011.6.561 
[14] 
Mathias Staudigl. A limit theorem for Markov decision processes. Journal of Dynamics and Games, 2014, 1 (4) : 639659. doi: 10.3934/jdg.2014.1.639 
[15] 
Meixin Xiong, Liuhong Chen, Ju Ming. Quantify uncertainty by estimating the probability density function of the output of interest using MLMC based Bayes method. Discrete and Continuous Dynamical Systems  B, 2022 doi: 10.3934/dcdsb.2022095 
[16] 
H.Thomas Banks, Shuhua Hu. Nonlinear stochastic Markov processes and modeling uncertainty in populations. Mathematical Biosciences & Engineering, 2012, 9 (1) : 125. doi: 10.3934/mbe.2012.9.1 
[17] 
Tatiana Filippova. Differential equations of ellipsoidal state estimates in nonlinear control problems under uncertainty. Conference Publications, 2011, 2011 (Special) : 410419. doi: 10.3934/proc.2011.2011.410 
[18] 
Nguyen Dinh Cong, Doan Thai Son, Stefan Siegmund, Hoang The Tuan. An instability theorem for nonlinear fractional differential systems. Discrete and Continuous Dynamical Systems  B, 2017, 22 (8) : 30793090. doi: 10.3934/dcdsb.2017164 
[19] 
ShuiHung Hou. On an application of fixed point theorem to nonlinear inclusions. Conference Publications, 2011, 2011 (Special) : 692697. doi: 10.3934/proc.2011.2011.692 
[20] 
Gábor Székelyhidi, Ben Weinkove. On a constant rank theorem for nonlinear elliptic PDEs. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 65236532. doi: 10.3934/dcds.2016081 
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