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On approximation of BSDE and multistep MLEprocesses
Laboratoire Manceau des Mathématiques, Université du Maine Le Mans, France and National Research University “MPEI”, Moscow, Russia 
References:
[1] 
Bismut, JM:Conjugate convex functions in optimal stochastic control. J. Math. Anal. Appl 44, 384404(1973), 
[2] 
El Karoui, N, Peng, S, Quenez, M:Backward stochastic differential equations in finance. Math. Fin 7, 171 (1997), 
[3] 
Fisher, RA:Theory of statistical estimation. Proc. Cambridge Phylosophical Society 22, 700725 (1925), 
[4] 
Freidlin, MI, Wentzell, AD Random Perturbations of Dynamical Systems, 2nd Ed. Springer, NY (1998), 
[5] 
Gasparyan, S, Kutoyants, YA:On approximation of the BSDE with unknown volatility in forward equation. Armenian J. Math 7(1), 5979 (2015), 
[6] 
Ibragimov, IA, Has'minskii, RZ:Statistical EstimationAsymptotic Theory. Springer, New York (1981), 
[7] 
Jeganathan, P:Some asymptotic properties of risk functions when the limit of the experiment is mixed normal. Sankhya:The Indian Journal of Statistics 45(Series A, Pt.1), 6687 (1983), 
[8] 
Kamatani, K, Uchida, M:Hybrid multistep estimators for stochastic differential equations based on sampled data. Statist. Inference Stoch. Processes 18(2), 177204 (2015), 
[9] 
Kutoyants, YA:Identification of Dynamical Systems with Small Noise. Kluwer Academic Publisher, Dordrecht (1994), 
[10] 
Kutoyants, YA:On approximation of the backward stochastic differential equation. Small noise, large samples and high frequency cases. Proceed. Steklov Inst. Mathematics 287, 133154 (2014), 
[11] 
Kutoyants, YA:On MultiStep MLEProcess for Ergodic Diffusion. arXiv:1504.01869[math.ST] (2015), 
[12] 
Kutoyants, YA, Motrunich, A:On miltistep MLEprocess for Markov sequences. Metrika 79(6), 705724(2016), 
[13] 
Kutoyants, YA, Zhou, L:On approximation of the backward stochastic differential equation.(arXiv:1305.3728). J. Stat. Plann. Infer 150, 111123 (2014), 
[14] 
Le Cam, L:On the asymptotic theory of estimation and testing hypotheses. Proc. 3rd Berkeley Symposium, vol. 1, pp. 129156 (1956), 
[15] 
Lehmann, EL, Romano, JP Testing Statistical Hypotheses, 3rd ed. Springer, NY (2005), 
[16] 
Liptser, R, Shiryaev, AN Statistics of Random Processes, v.'s 1 and 2, 2nd ed. Springer, NY (2001), 
[17] 
Pardoux, E, Peng, S:Adapted solution of a backward stochastic differential equation. System Control Letter 14, 5561 (1990), 
[18] 
Pardoux, E, Peng, S:Backward stochastic differential equations and quasilinear parabolic partial differential equations. Stochastic Partial Differential Equations and their Applications, pp. 200217. Springer, Berlin (1992). (Lect. Notes Control Inf. Sci. 176), 
[19] 
Robinson, PM:The stochastic difference between econometric statistics. Econometrica 56(3), 531548(1988), 
[20] 
Skorohod, AV, Khasminskii, RZ:On parameter estimation by indirect observations. Prob. Inform. Transm 32, 5868 (1996), 
[21] 
Uchida, M, Yoshida, N:Adaptive Bayes type estimators of ergodic diffusion processes from discrete observations. Statist. Inference Stoch. Processes 17(2), 181219 (2014), 
show all references
References:
[1] 
Bismut, JM:Conjugate convex functions in optimal stochastic control. J. Math. Anal. Appl 44, 384404(1973), 
[2] 
El Karoui, N, Peng, S, Quenez, M:Backward stochastic differential equations in finance. Math. Fin 7, 171 (1997), 
[3] 
Fisher, RA:Theory of statistical estimation. Proc. Cambridge Phylosophical Society 22, 700725 (1925), 
[4] 
Freidlin, MI, Wentzell, AD Random Perturbations of Dynamical Systems, 2nd Ed. Springer, NY (1998), 
[5] 
Gasparyan, S, Kutoyants, YA:On approximation of the BSDE with unknown volatility in forward equation. Armenian J. Math 7(1), 5979 (2015), 
[6] 
Ibragimov, IA, Has'minskii, RZ:Statistical EstimationAsymptotic Theory. Springer, New York (1981), 
[7] 
Jeganathan, P:Some asymptotic properties of risk functions when the limit of the experiment is mixed normal. Sankhya:The Indian Journal of Statistics 45(Series A, Pt.1), 6687 (1983), 
[8] 
Kamatani, K, Uchida, M:Hybrid multistep estimators for stochastic differential equations based on sampled data. Statist. Inference Stoch. Processes 18(2), 177204 (2015), 
[9] 
Kutoyants, YA:Identification of Dynamical Systems with Small Noise. Kluwer Academic Publisher, Dordrecht (1994), 
[10] 
Kutoyants, YA:On approximation of the backward stochastic differential equation. Small noise, large samples and high frequency cases. Proceed. Steklov Inst. Mathematics 287, 133154 (2014), 
[11] 
Kutoyants, YA:On MultiStep MLEProcess for Ergodic Diffusion. arXiv:1504.01869[math.ST] (2015), 
[12] 
Kutoyants, YA, Motrunich, A:On miltistep MLEprocess for Markov sequences. Metrika 79(6), 705724(2016), 
[13] 
Kutoyants, YA, Zhou, L:On approximation of the backward stochastic differential equation.(arXiv:1305.3728). J. Stat. Plann. Infer 150, 111123 (2014), 
[14] 
Le Cam, L:On the asymptotic theory of estimation and testing hypotheses. Proc. 3rd Berkeley Symposium, vol. 1, pp. 129156 (1956), 
[15] 
Lehmann, EL, Romano, JP Testing Statistical Hypotheses, 3rd ed. Springer, NY (2005), 
[16] 
Liptser, R, Shiryaev, AN Statistics of Random Processes, v.'s 1 and 2, 2nd ed. Springer, NY (2001), 
[17] 
Pardoux, E, Peng, S:Adapted solution of a backward stochastic differential equation. System Control Letter 14, 5561 (1990), 
[18] 
Pardoux, E, Peng, S:Backward stochastic differential equations and quasilinear parabolic partial differential equations. Stochastic Partial Differential Equations and their Applications, pp. 200217. Springer, Berlin (1992). (Lect. Notes Control Inf. Sci. 176), 
[19] 
Robinson, PM:The stochastic difference between econometric statistics. Econometrica 56(3), 531548(1988), 
[20] 
Skorohod, AV, Khasminskii, RZ:On parameter estimation by indirect observations. Prob. Inform. Transm 32, 5868 (1996), 
[21] 
Uchida, M, Yoshida, N:Adaptive Bayes type estimators of ergodic diffusion processes from discrete observations. Statist. Inference Stoch. Processes 17(2), 181219 (2014), 
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