# 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

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topCox, 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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