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On one property of martingales with conditionally Gaussian increments and its application in the theory of nonasymptotic inference

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Abstract

A transformation of a discrete-time martingale with conditionally Gaussian increments into a sequence of i.i.d. standard Gaussian random variables is proposed as based on a sequence of stopping times constructed using the quadratic variation. It is shown that sequential estimators for the parameters in AR(1) and generalized first-order autoregressive models have a nonasymptotic normal distribution.

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Authors and Affiliations

  1. National Research Tomsk State University, Tomsk, 634050, Russia

    V. V. Konev

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  1. V. V. Konev
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Correspondence to V. V. Konev.

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Original Russian Text © V.V. Konev, 2016, published in Doklady Akademii Nauk, 2016, Vol. 471, No. 5, pp. 523–527.

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Konev, V.V. On one property of martingales with conditionally Gaussian increments and its application in the theory of nonasymptotic inference. Dokl. Math. 94, 676–680 (2016). https://doi.org/10.1134/S1064562416060235

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  • DOI: https://doi.org/10.1134/S1064562416060235

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