January  2016, 1: 5 doi: 10.1186/s41546-016-0006-z

Editorial

1 Shandong University, Ji'nan, China;

2 Université de Bretagne Occidentale, Brest, France;

3 Shandong University, Weihai, China

Received  July 05, 2016 Revised  July 05, 2016 Published  August 2016

Fund Project: This work was done with partial financial support of the RSF grant number 14-49-10079

Citation: Shige Peng, Rainer Buckdahn, Juan Li. Editorial. Probability, Uncertainty and Quantitative Risk, 2016, 1 (0) : 5-. doi: 10.1186/s41546-016-0006-z
References:
[1]

Bismut, JM:Conjugate convex functions in optimal stochastic control. J. Math. Anal. Appl 44, 384-404(1973) Google Scholar

[2]

El Karoui, N, Peng, S, Quenez, M:Backward stochastic differential equations in finance. Math. Fin 7, 1-71 (1997) Google Scholar

[3]

Fisher, RA:Theory of statistical estimation. Proc. Cambridge Phylosophical Society 22, 700-725 (1925) Google Scholar

[4]

Freidlin, MI, Wentzell, AD Random Perturbations of Dynamical Systems, 2nd Ed. Springer, NY (1998) Google Scholar

[5]

Gasparyan, S, Kutoyants, YA:On approximation of the BSDE with unknown volatility in forward equation. Armenian J. Math 7(1), 59-79 (2015) Google Scholar

[6]

Ibragimov, IA, Has'minskii, RZ:Statistical Estimation-Asymptotic Theory. Springer, New York (1981) Google Scholar

[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), 66-87 (1983) Google Scholar

[8]

Kamatani, K, Uchida, M:Hybrid multi-step estimators for stochastic differential equations based on sampled data. Statist. Inference Stoch. Processes 18(2), 177-204 (2015) Google Scholar

[9]

Kutoyants, YA:Identification of Dynamical Systems with Small Noise. Kluwer Academic Publisher, Dordrecht (1994) Google Scholar

[10]

Kutoyants, YA:On approximation of the backward stochastic differential equation. Small noise, large samples and high frequency cases. Proceed. Steklov Inst. Mathematics 287, 133-154 (2014) Google Scholar

[11]

Kutoyants, YA:On Multi-Step MLE-Process for Ergodic Diffusion. arXiv:1504.01869[math.ST] (2015) Google Scholar

[12]

Kutoyants, YA, Motrunich, A:On milti-step MLE-process for Markov sequences. Metrika 79(6), 705-724(2016) Google Scholar

[13]

Kutoyants, YA, Zhou, L:On approximation of the backward stochastic differential equation.(arXiv:1305.3728). J. Stat. Plann. Infer 150, 111-123 (2014) Google Scholar

[14]

Le Cam, L:On the asymptotic theory of estimation and testing hypotheses. Proc. 3rd Berkeley Symposium, vol. 1, pp. 129-156 (1956) Google Scholar

[15]

Lehmann, EL, Romano, JP Testing Statistical Hypotheses, 3rd ed. Springer, NY (2005) Google Scholar

[16]

Liptser, R, Shiryaev, AN Statistics of Random Processes, v.'s 1 and 2, 2-nd ed. Springer, NY (2001) Google Scholar

[17]

Pardoux, E, Peng, S:Adapted solution of a backward stochastic differential equation. System Control Letter 14, 55-61 (1990) Google Scholar

[18]

Pardoux, E, Peng, S:Backward stochastic differential equations and quasilinear parabolic partial differential equations. Stochastic Partial Differential Equations and their Applications, pp. 200-217. Springer, Berlin (1992). (Lect. Notes Control Inf. Sci. 176) Google Scholar

[19]

Robinson, PM:The stochastic difference between econometric statistics. Econometrica 56(3), 531-548(1988) Google Scholar

[20]

Skorohod, AV, Khasminskii, RZ:On parameter estimation by indirect observations. Prob. Inform. Transm 32, 58-68 (1996) Google Scholar

[21]

Uchida, M, Yoshida, N:Adaptive Bayes type estimators of ergodic diffusion processes from discrete observations. Statist. Inference Stoch. Processes 17(2), 181-219 (2014) Google Scholar

show all references

References:
[1]

Bismut, JM:Conjugate convex functions in optimal stochastic control. J. Math. Anal. Appl 44, 384-404(1973) Google Scholar

[2]

El Karoui, N, Peng, S, Quenez, M:Backward stochastic differential equations in finance. Math. Fin 7, 1-71 (1997) Google Scholar

[3]

Fisher, RA:Theory of statistical estimation. Proc. Cambridge Phylosophical Society 22, 700-725 (1925) Google Scholar

[4]

Freidlin, MI, Wentzell, AD Random Perturbations of Dynamical Systems, 2nd Ed. Springer, NY (1998) Google Scholar

[5]

Gasparyan, S, Kutoyants, YA:On approximation of the BSDE with unknown volatility in forward equation. Armenian J. Math 7(1), 59-79 (2015) Google Scholar

[6]

Ibragimov, IA, Has'minskii, RZ:Statistical Estimation-Asymptotic Theory. Springer, New York (1981) Google Scholar

[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), 66-87 (1983) Google Scholar

[8]

Kamatani, K, Uchida, M:Hybrid multi-step estimators for stochastic differential equations based on sampled data. Statist. Inference Stoch. Processes 18(2), 177-204 (2015) Google Scholar

[9]

Kutoyants, YA:Identification of Dynamical Systems with Small Noise. Kluwer Academic Publisher, Dordrecht (1994) Google Scholar

[10]

Kutoyants, YA:On approximation of the backward stochastic differential equation. Small noise, large samples and high frequency cases. Proceed. Steklov Inst. Mathematics 287, 133-154 (2014) Google Scholar

[11]

Kutoyants, YA:On Multi-Step MLE-Process for Ergodic Diffusion. arXiv:1504.01869[math.ST] (2015) Google Scholar

[12]

Kutoyants, YA, Motrunich, A:On milti-step MLE-process for Markov sequences. Metrika 79(6), 705-724(2016) Google Scholar

[13]

Kutoyants, YA, Zhou, L:On approximation of the backward stochastic differential equation.(arXiv:1305.3728). J. Stat. Plann. Infer 150, 111-123 (2014) Google Scholar

[14]

Le Cam, L:On the asymptotic theory of estimation and testing hypotheses. Proc. 3rd Berkeley Symposium, vol. 1, pp. 129-156 (1956) Google Scholar

[15]

Lehmann, EL, Romano, JP Testing Statistical Hypotheses, 3rd ed. Springer, NY (2005) Google Scholar

[16]

Liptser, R, Shiryaev, AN Statistics of Random Processes, v.'s 1 and 2, 2-nd ed. Springer, NY (2001) Google Scholar

[17]

Pardoux, E, Peng, S:Adapted solution of a backward stochastic differential equation. System Control Letter 14, 55-61 (1990) Google Scholar

[18]

Pardoux, E, Peng, S:Backward stochastic differential equations and quasilinear parabolic partial differential equations. Stochastic Partial Differential Equations and their Applications, pp. 200-217. Springer, Berlin (1992). (Lect. Notes Control Inf. Sci. 176) Google Scholar

[19]

Robinson, PM:The stochastic difference between econometric statistics. Econometrica 56(3), 531-548(1988) Google Scholar

[20]

Skorohod, AV, Khasminskii, RZ:On parameter estimation by indirect observations. Prob. Inform. Transm 32, 58-68 (1996) Google Scholar

[21]

Uchida, M, Yoshida, N:Adaptive Bayes type estimators of ergodic diffusion processes from discrete observations. Statist. Inference Stoch. Processes 17(2), 181-219 (2014) Google Scholar

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