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On the Strong Law of Large Numbers for Multivariate Martingales with Continuous Time

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Ukrainian Mathematical Journal Aims and scope

Abstract

We prove the strong law of large numbers for vector martingales with arbitrary operator normalizations. From the theorem proved, we deduce several known results on the strong law of large numbers for martingales with continuous time.

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REFERENCES

  1. A. V. Mel'nikov, “Law of large numbers for multivariate martingales,” Dokl. Akad. Nauk SSSR, 286, No. 3, 546–550 (1986).

    Google Scholar 

  2. A. V. Mel'nikov, “Stochastic differential equations: nonsmoothness of coefficients, regression models, and stochastic approximation,” Usp. Mat. Nauk, 51, No. 5, 43–136 (1996).

    Google Scholar 

  3. A. Le Breton and M. Musiela, “Laws of large numbers for semimartingales with applications to stochastic regression,” Probab. Theor. Rel. Fields, 81, No. 2, 275–290 (1989).

    Google Scholar 

  4. K. Dzhaparidze and P. Spreij, “The strong law of large numbers for martingales with deterministic quadratic variation,” Stoch. Rep., 42, No. 1, 53–65 (1993).

    Google Scholar 

  5. Y.-X. Lin, “On the strong law of large numbers for multivariate martingales with random norming,” Stoch. Proc. Appl., 54, No. 3, 355–360 (1994).

    Google Scholar 

  6. V. V. Buldygin and S. A. Solntsev, Functional Methods in Problems of Summation of Random Variables [in Russian], Naukova Dumka, Kiev (1989).

    Google Scholar 

  7. V. O. Koval', “Limit theorems for operator-normalized random vectors. I,” Teor. Imov. Mat. Statist., Issue 61, 47–58 (1999).

  8. R. Sh. Liptser and A. N. Shiryaev, Theory of Martingales [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  9. M. Duflo, Random Iterative Models, Springer, Berlin (1997).

    Google Scholar 

  10. H. Kaufmann, “On the strong law of large numbers for multivariate martingales,” Stoch. Proc. Appl., 26, No. 1, 73–85 (1987).

    Google Scholar 

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Authors and Affiliations

  1. Kiev Polytechnic Institute, Kiev

    V. A. Koval'

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  1. V. A. Koval'
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Koval', V.A. On the Strong Law of Large Numbers for Multivariate Martingales with Continuous Time. Ukrainian Mathematical Journal 53, 1554–1560 (2001). https://doi.org/10.1023/A:1014379027748

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  • DOI: https://doi.org/10.1023/A:1014379027748

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