Comptes Rendus
Probability theory/Optimal control
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.

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.

Published online:
DOI: 10.1016/j.crma.2019.02.007

Yuta Yaegashi 1; Hidekazu Yoshioka 2; Kentaro Tsugihashi 2; Masayuki Fujihara 1

1 Graduate School of Agriculture, Kyoto University, Kitashirakawa Oiwake-cho, Sakyo-ku, Kyoto City, Kyoto Prefecture, 606-8502, Japan
2 Graduate School of Natural Science and Technology, Shimane University, Nishikawatsu-cho 1060, Matsue City, Shimane Prefecture, 690-8504, Japan
     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},
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.

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