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Strong Approximation of Locally Square-Integrable Martingales

Strong Approximation of Locally Square-Integrable Martingales
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摘要 In this paper, we consider the strong approximation for locally square-integrable martingales. In our results, the limit process may be a process with jumps. This is an extension of the former results. In this paper, we consider the strong approximation for locally square-integrable martingales. In our results, the limit process may be a process with jumps. This is an extension of the former results.
作者 Zheng Yan LIN Han Chao WANG
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第6期1221-1232,共12页 数学学报（英文版）
基金 Supported by National Natural Science Foundation of China (Grant No. 10871177) Specialized Research Fund for the Doctor Program of Higher Education (Grant No. 20090101110020)
关键词 Locally square-integrable martingales strong approximation JUMPS Locally square-integrable martingales, strong approximation, jumps
分类号 O211.6 [理学—概率论与数理统计] O211.4 [理学—概率论与数理统计]
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参考文献10

  • 1Liu, W., Lin, Z.: Strong approximation for a class of stationary processes. Stochastic Process. Appl., 119, 249-280 (2009).
  • 2Berkes, I., HSrmann, S., Schauer, J.: Asymptotic results for the empirical process of stationary sequences. Stochastic Process. Appl., 119, 1298-1324 (2009).
  • 3Yang, X., Liu, W., Fu, K., Zhang, L.: Convergence rates of tail probabilities for sums under dependence assumptions. Acta Mathematica Sinica, English Series, 26, 1591-1600 (2010).
  • 4Eberlein, E.: Strong approximation of continuous time stochastic processes. J. Multivariate Anal., 31, 115-137 (1989).
  • 5Besdziek, N.: Strong approximations of semimartingales by processes with independent increments. Probab. Theory Related Fields, 87, 489-520 (1991).
  • 6Eberlein, E., Romersperger, M.: Strong approximation of semimartingales and statistical processes. Probab. Theory Related Fields, 104, 539-567 (1996).
  • 7Jacod, J., Shiryaev, A. N.: Limit Theorems for Stochastic Processes, Springer, New York, 2003.
  • 8Jacod, J.: Calcus Stochastique et Problbmes de Martingales. Lecture Notes in Math. Vol. 714, Springer, Berlin Heidelberg, New York, 1979.
  • 9He, S., Wang, J., Yan, J.: Semimartingale Theory and Stochastic Calculus, Science Press and CRC Press, Beijing and Boca Raton, 1992.
  • 10Rebolledo, R.: La methode des martingales appliquee a l'etude de la convergence en loi de processus. Bull. Soc. Math. France Mem., 62, 1-125 (1979).
Acta Mathematica Sinica,English Series
2012年 第6期

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