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.
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.
Accepted:
Published online:
Yuta Yaegashi 1; Hidekazu Yoshioka 2; Kentaro Tsugihashi 2; Masayuki Fujihara 1
@article{CRMATH_2019__357_3_306_0,
author = {Yuta Yaegashi and Hidekazu Yoshioka and Kentaro Tsugihashi and Masayuki Fujihara},
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},
}
TY - JOUR AU - Yuta Yaegashi AU - Hidekazu Yoshioka AU - Kentaro Tsugihashi AU - Masayuki Fujihara 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 DO - 10.1016/j.crma.2019.02.007 LA - en ID - CRMATH_2019__357_3_306_0 ER -
%0 Journal Article %A Yuta Yaegashi %A Hidekazu Yoshioka %A Kentaro Tsugihashi %A Masayuki Fujihara %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 %R 10.1016/j.crma.2019.02.007 %G en %F CRMATH_2019__357_3_306_0
Yuta Yaegashi; Hidekazu Yoshioka; Kentaro Tsugihashi; Masayuki Fujihara. Analysis and computation of probability density functions for a 1-D impulsively controlled diffusion process. Comptes Rendus. Mathématique, Volume 357 (2019) no. 3, pp. 306-315. doi : 10.1016/j.crma.2019.02.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2019.02.007/
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