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When is a stochastic integral a time change of a diffusion?

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Abstract

We give necessary and sufficient conditions that a time change of ann-dimensional Ito stochastic integralX t of the form

$$dX_t = u(t,\omega )dt + v(t,\omega )dB_t $$

leads to a process with the same law as a diffusionY t of the form

$$dY_t = b(Y_t )dt + \sigma (Y_t )dB_t $$

where the generatorA ofY t is assumed to have a unique solution of the martingale problem. The result has applications to conformal martingales in ℂn and harmonic morphisms.

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Authors and Affiliations

  1. Department of Mathematics, University of Oslo, Blindern, Box 1053, N-0316, Oslo 3, Norway

    Bernt Øksendal

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  1. Bernt Øksendal
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Øksendal, B. When is a stochastic integral a time change of a diffusion?. J Theor Probab 3, 207–226 (1990). https://doi.org/10.1007/BF01045159

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  • DOI: https://doi.org/10.1007/BF01045159

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