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

Alexander M.G. Cox; David Hobson; Jan Obłój

ESAIM: Probability and Statistics (2011)

  • Volume: 15, page S11-S24
  • ISSN: 1292-8100

Abstract

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We solve explicitly the following problem: for a given probability measure μ, we specify a generalised martingale diffusion (Xt) which, stopped at an independent exponential time T, is distributed according to μ. The process (Xt) 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.

How to cite

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Cox, Alexander M.G., Hobson, David, and Obłój, Jan. "Time-homogeneous diffusions with a given marginal at a random time." ESAIM: Probability and Statistics 15 (2011): S11-S24. <http://eudml.org/doc/197757>.

@article{Cox2011,
abstract = { We solve explicitly the following problem: for a given probability measure μ, we specify a generalised martingale diffusion (Xt) which, stopped at an independent exponential time T, is distributed according to μ. The process (Xt) 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. },
author = {Cox, Alexander M.G., Hobson, David, Obłój, Jan},
journal = {ESAIM: Probability and Statistics},
keywords = {Time-homogeneous diffusion; generalised diffusion; exponential time; Skorokhod embedding problem; Bertoin-Le Jan stopping time},
language = {eng},
month = {5},
pages = {S11-S24},
publisher = {EDP Sciences},
title = {Time-homogeneous diffusions with a given marginal at a random time},
url = {http://eudml.org/doc/197757},
volume = {15},
year = {2011},
}

TY - JOUR
AU - Cox, Alexander M.G.
AU - Hobson, David
AU - Obłój, Jan
TI - Time-homogeneous diffusions with a given marginal at a random time
JO - ESAIM: Probability and Statistics
DA - 2011/5//
PB - EDP Sciences
VL - 15
SP - S11
EP - S24
AB - We solve explicitly the following problem: for a given probability measure μ, we specify a generalised martingale diffusion (Xt) which, stopped at an independent exponential time T, is distributed according to μ. The process (Xt) 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.
LA - eng
KW - Time-homogeneous diffusion; generalised diffusion; exponential time; Skorokhod embedding problem; Bertoin-Le Jan stopping time
UR - http://eudml.org/doc/197757
ER -

References

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