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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2019.02.007
Yaegashi, Yuta 1; Yoshioka, Hidekazu 2; Tsugihashi, Kentaro 2; Fujihara, Masayuki 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
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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, Volume 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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