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PDE for joint law of the pair of a continuous diffusion and its running maximum

Abstract : Let X be a d-dimensional diffusion process and M the running supremum of the first component. In this paper, in case of dimension d, we first show that for any t > 0, the law of the pair (M t , X t) admits a density with respect to Lebesgue measure. In uni-dimensional case, we compute this one. This allows us to show that for any t > 0, the pair formed by the random variable X t and the running supremum M t of X at time t can be characterized as a solution of a weakly valued-measure partial differential equation.
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https://hal.archives-ouvertes.fr/hal-01591946
Contributor : Monique Pontier <>
Submitted on : Friday, September 22, 2017 - 12:32:11 PM
Last modification on : Thursday, March 5, 2020 - 5:55:40 PM
Long-term archiving on: : Saturday, December 23, 2017 - 1:45:51 PM

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  • HAL Id : hal-01591946, version 1

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Laure Coutin, Monique Pontier. PDE for joint law of the pair of a continuous diffusion and its running maximum. 2017. ⟨hal-01591946⟩

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