Journal of Theoretical Probability

, Volume 3, Issue 2, pp 207–226 | Cite as

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

  • Bernt Øksendal


We give necessary and sufficient conditions that a time change of ann-dimensional Ito stochastic integralXt of the form
$$dX_t = u(t,\omega )dt + v(t,\omega )dB_t $$
leads to a process with the same law as a diffusionYt of the form
$$dY_t = b(Y_t )dt + \sigma (Y_t )dB_t $$
where the generatorA ofYt is assumed to have a unique solution of the martingale problem. The result has applications to conformal martingales in ℂ n and harmonic morphisms.

Key Words

Stochastic integral diffusion conformal martingales 


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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • Bernt Øksendal
    • 1
  1. 1.Department of MathematicsUniversity of OsloOslo 3Norway

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