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Strong approximations of semimartingales by processes with independent increments
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  • Published: December 1991

Strong approximations of semimartingales by processes with independent increments

  • N. Besdziek1 

Probability Theory and Related Fields volume 87, pages 489–520 (1991)Cite this article

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Summary

Strong approximation theorems for continuous time semimartingales are obtained by combining some techniques of the general theory of stochastic processes with some of the direct approximation of dependent random variables by independent ones. Continuous processes with independent increments whose variance functions increase polynomially or exponentially are considered as approximating processes. The basic assumptions of the main results only contain rates of convergence for certain probabilities. In particular, moment assumptions are not required. Some almost sure invariance principles for partial sum processes with nonlinear growth of variance and for functionals of Markov processes are derived by applying the main results.

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Authors and Affiliations

  1. Institut für Mathematische Stochastik, Universität Freiburg, W-7800, Freiburg, Federal Republic of Germany

    N. Besdziek

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  1. N. Besdziek
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Besdziek, N. Strong approximations of semimartingales by processes with independent increments. Probab. Th. Rel. Fields 87, 489–520 (1991). https://doi.org/10.1007/BF01304277

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  • Received: 14 March 1990

  • Revised: 12 September 1990

  • Issue Date: December 1991

  • DOI: https://doi.org/10.1007/BF01304277

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Keywords

  • Stochastic Process
  • General Theory
  • Markov Process
  • Mathematical Biology
  • Basic Assumption
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