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3 results

  • On coupling of diffusion processes

  • Torgny Lindvall
  • Journal:
    Journal of Applied Probability / Volume 20 / Issue 1 / March 1983
    Published online by Cambridge University Press:
    14 July 2016, pp. 82-93
    Print publication:
    March 1983

  • The coupling method is well fitted to be used in the study of the asymptotics of one-dimensional diffusion processes. We give an elementary proof of Orey's theorem in the recurrent case, and establish rate results for tendency towards equilibrium under moment conditions on the speed measure and the initial distributions.

  • On Coupling of continuous-time renewal processes

  • Torgny Lindvall
  • Journal:
    Journal of Applied Probability / Volume 19 / Issue 1 / March 1982
    Published online by Cambridge University Press:
    14 July 2016, pp. 82-89
    Print publication:
    March 1982

  • This paper shows how the coupling method applies to renewal theory in continuous time. Old and new rate results for tendency towards equilibrium and forgetfulness of initial delay are obtained. The coupling approach also provides a new way of analysing the asymptotics of functions of renewal processes which avoids the route via a renewal equation.