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Embedding in Brownian motion with drift and the Azéma-Yor construction

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  • Grandits, Peter
  • Falkner, Neil

Abstract

We consider the embedding of a probability distribution in Brownian motion with drift. We first give a sufficient condition on the target measure, under which a variant of the Azéma-Yor (1979a, Séminaire de Probabilités XIII, Lecture Notes in Mathematics, Vol. 721, Springer, Berlin, pp. 90-115) construction for this problem works. A necessary and sufficient condition for embeddability by means of some stopping time, not necessarily finite, is also provided. This latter condition is then analyzed in some detail.

Suggested Citation

  • Grandits, Peter & Falkner, Neil, 2000. "Embedding in Brownian motion with drift and the Azéma-Yor construction," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 249-254, February.
    • Handle: RePEc:eee:spapps:v:85:y:2000:i:2:p:249-254
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    Cited by:

    1. Pedersen, J. L. & Peskir, G., 2001. "The Azéma-Yor embedding in non-singular diffusions," Stochastic Processes and their Applications, Elsevier, vol. 96(2), pages 305-312, December.
    2. Cox, A. M. G. & Hobson, D. G., 2004. "An optimal Skorokhod embedding for diffusions," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 17-39, May.

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