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

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY Advances in Applied Probability Pub Date : 2023-01-06 DOI:10.1017/apr.2022.76

L. Coutin, M. Pontier

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引用次数: 2

Abstract

Let X be a d-dimensional diffusion and M the running supremum of its first component. In this paper, we show that for any

$t>0,$

the density (with respect to the

$(d+1)$

-dimensional Lebesgue measure) of the pair

$\big(M_t,X_t\big)$

is a weak solution of a Fokker–Planck partial differential equation on the closed set

$\big\{(m,x)\in \mathbb{R}^{d+1},\,{m\geq x^1}\big\},$

using an integral expansion of this density.

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PDE为连续扩散对及其运行最大值的联合律

设X是d维扩散，M是其第一个分量的运行上确界。在本文中，我们证明了对于任何$t>0，$对$\big（M_t，X_t\big）$的密度（相对于$（d+1）$维Lebesgue测度）是闭集$\big上的Fokker–Planck偏微分方程的弱解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Applied Probability 数学-统计学与概率论

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Advances in Applied Probability has been published by the Applied Probability Trust for over four decades, and is a companion publication to the Journal of Applied Probability. It contains mathematical and scientific papers of interest to applied probabilists, with emphasis on applications in a broad spectrum of disciplines, including the biosciences, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.