Time-homogeneous diffusions with a given marginal at a random time

Alexander M G Cox, David Hobson, Jan Obłój

Research output: Contribution to journalArticle

13 Citations (Scopus)
112 Downloads (Pure)

Abstract

We solve explicitly the following problem: for a given probability measure μ, we specify a generalised martingale diffusion (X_t) which, stopped at an independent exponential time T, is distributed according to μ. The process (X_t) is specified via its speed measure m. We present two heuristic arguments and three proofs. First we show how the result can be derived from the solution of [Bertoin and Le Jan, Ann. Probab. 20 (1992) 538–548.] to the Skorokhod embedding problem. Secondly, we give a proof exploiting applications of Krein's spectral theory of strings to the study of linear diffusions. Finally, we present a novel direct probabilistic proof based on a coupling argument.
Original languageEnglish
Pages (from-to)S11-S24
JournalESAIM: Probability and Statistics
Volume15
DOIs
Publication statusPublished - Feb 2011

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