[Analyse et calcul des fonctions de densité de probabilité pour un processus de diffusion en dimension 1 contrôlé par impulsion]
Cette Note propose des conditions aux limites appropriées pour l'équation de Kolmogorov antérograde gouvernant une fonction de densité de probabilité stationnaire d'un processus de diffusion contrôlé par impulsion, en dimension 1. Nous obtenons une fonction de densité de probabilité exacte. La condition aux limites est vérifiée numériquement pour l'approche de Monte Carlo. Nous présentons également une méthode de volumes finis pour résoudre l'équation et nous étudions sa précision au moyen de simulations numériques.
This paper proposes appropriate boundary conditions to be equipped with Kolmogorov's Forward Equation that governs a stationary probability density function for a 1-D impulsively controlled diffusion process and derives an exact probability density function. The boundary conditions are verified numerically with a Monte Carlo approach. A finite-volume method for solving the equation is also presented and its accuracy is investigated through numerical experiments.
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@article{CRMATH_2019__357_3_306_0,
author = {Yaegashi, Yuta and Yoshioka, Hidekazu and Tsugihashi, Kentaro and Fujihara, Masayuki},
title = {Analysis and computation of probability density functions for a {1-D} impulsively controlled diffusion process},
journal = {Comptes Rendus. Math\'ematique},
pages = {306--315},
publisher = {Elsevier},
volume = {357},
number = {3},
year = {2019},
doi = {10.1016/j.crma.2019.02.007},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2019.02.007/}
}
TY - JOUR AU - Yaegashi, Yuta AU - Yoshioka, Hidekazu AU - Tsugihashi, Kentaro AU - Fujihara, Masayuki TI - Analysis and computation of probability density functions for a 1-D impulsively controlled diffusion process JO - Comptes Rendus. Mathématique PY - 2019 SP - 306 EP - 315 VL - 357 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2019.02.007/ DO - 10.1016/j.crma.2019.02.007 LA - en ID - CRMATH_2019__357_3_306_0 ER -
%0 Journal Article %A Yaegashi, Yuta %A Yoshioka, Hidekazu %A Tsugihashi, Kentaro %A Fujihara, Masayuki %T Analysis and computation of probability density functions for a 1-D impulsively controlled diffusion process %J Comptes Rendus. Mathématique %D 2019 %P 306-315 %V 357 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2019.02.007/ %R 10.1016/j.crma.2019.02.007 %G en %F CRMATH_2019__357_3_306_0
Yaegashi, Yuta; Yoshioka, Hidekazu; Tsugihashi, Kentaro; Fujihara, Masayuki. Analysis and computation of probability density functions for a 1-D impulsively controlled diffusion process. Comptes Rendus. Mathématique, Tome 357 (2019) no. 3, pp. 306-315. doi : 10.1016/j.crma.2019.02.007. http://www.numdam.org/articles/10.1016/j.crma.2019.02.007/
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