Mario Lefebvre
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Solutions de similitude d'un jeu différentiel stochastique
arima:1864 -
Revue Africaine de Recherche en Informatique et Mathématiques Appliquées,
November 29, 2006,
Volume 5, Special Issue TAM TAM'05, november 2006
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https://doi.org/10.46298/arima.1864
Solutions de similitude d'un jeu différentiel stochastiqueArticle
Authors: Mario Lefebvre 1
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Mario Lefebvre
1 Département de Mathématiques et de Génie Industriel
A two-dimensional controlled stochastic process defined by a set of stochastic differential equations is considered. Contrary to the most frequent formulation, the control variables appear only in the infinitesimal variances of the process, rather than in the infinitesimal means. The differential game ends the first time the two controlled processes are equal or their difference is equal to a given constant. Explicit solutions to particular problems are obtained by making use of the method of similarity solutions to solve the appropriate partial differential equation.