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Martingales and the Robbins-Monro procedure in D[0, 1]

Listed author(s):
  • Walk, H.
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    The Robbins-Monro procedure for recursive estimation of a zero point of a regression function f is investigated for the case f defined on and with values in the space D[0, 1] of real-valued functions on [0, 1] that are right-continuous and have left-hand limits, endowed with Skorohod's J1-topology. There are proved an a.s. convergence result and an invariance principle where the limit process is a Gaussian Markov process with paths in the space of continuous C[0, 1]-valued functions on [0, 1]. At first the case f(x) [reverse not equivalent] x, i.e., the case of a martingale in D[0, 1], is treated and by this then the general case. An application to an initial value problem with only empirically available function values is sketched.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 8 (1978)
    Issue (Month): 3 (September)
    Pages: 430-452

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    Handle: RePEc:eee:jmvana:v:8:y:1978:i:3:p:430-452
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