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Some local results on the convergence and the quadratic variation of random sequences
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  • Published: June 1990

Some local results on the convergence and the quadratic variation of random sequences

  • Nadjib Bouzar1 

Probability Theory and Related Fields volume 86, pages 265–275 (1990)Cite this article

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Summary

In this paper we study the following property\(P\) of a random sequence (X n ,n∈ℕ):X n converges a.s. to a finite limit and its quadratic variation is finite a.s. Several local results on the property\(P\) are established for random sequences satisfying

$$E\left( {X_{n + 1} |T_n } \right) \leqq X_n + h_n $$

where (h n ,n∈ℕ) is a random sequence. As an application random sequences taking values in a closed, possibly unbounded, interval of— are studied.

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Authors and Affiliations

  1. Department of Mathematics, Kuwait University, P.O. Box 5969, 13060, Kuwait, Kuwait

    Nadjib Bouzar

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  1. Nadjib Bouzar
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Bouzar, N. Some local results on the convergence and the quadratic variation of random sequences. Probab. Th. Rel. Fields 86, 265–275 (1990). https://doi.org/10.1007/BF01474646

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  • Received: 26 April 1989

  • Revised: 20 December 1989

  • Issue Date: June 1990

  • DOI: https://doi.org/10.1007/BF01474646

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Keywords

  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
  • Random Sequence
  • Local Result
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