Geodesic
Optimal solutions for inclusions of geometric Brownian motion type with mean derivatives
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 3, pp. 38-50

Voir la notice de l'article provenant de la source Math-Net.Ru

The idea of mean derivatives of stochastic processes was suggested by E. Nelson in 60-th years of XX century. Unlike ordinary derivatives, the mean derivatives are well-posed for a very broad class of stochastic processes and equations with mean derivatives naturally arise in many mathematical models of physics (in particular, E. Nelson introduced the mean derivatives for the needs of Stochastic Mechanics, a version of quantum mechanics). Inclusions with mean derivatives is a natural generalization of those equations in the case of feedback control or in motion in complicated media. The paper is devoted to a brief introduction into the theory of equations and inclusions with mean derivatives and to investigation of a special type of such inclusions called inclusions of geometric Brownian motion type. The existence of optimal solutions maximizing a certain cost criterion, is proved.
Keywords: mean derivatives; stochastic differential inclusions; optimal solution. 
@article{VYURU_2013_6_3_a3,
     author = {Yu. E. Gliklikh and O. O. Zheltikova},
     title = {Optimal solutions for inclusions of geometric {Brownian} motion type with mean derivatives},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {38--50},
     publisher = {mathdoc},
     volume = {6},
     number = {3},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2013_6_3_a3/}
}
TY  - JOUR
AU  - Yu. E. Gliklikh
AU  - O. O. Zheltikova
TI  - Optimal solutions for inclusions of geometric Brownian motion type with mean derivatives
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
PY  - 2013
SP  - 38
EP  - 50
VL  - 6
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VYURU_2013_6_3_a3/
LA  - en
ID  - VYURU_2013_6_3_a3
ER  - 
%0 Journal Article
%A Yu. E. Gliklikh
%A O. O. Zheltikova
%T Optimal solutions for inclusions of geometric Brownian motion type with mean derivatives
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie
%D 2013
%P 38-50
%V 6
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VYURU_2013_6_3_a3/
%G en
%F VYURU_2013_6_3_a3
Yu. E. Gliklikh; O. O. Zheltikova. Optimal solutions for inclusions of geometric Brownian motion type with mean derivatives. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 6 (2013) no. 3, pp. 38-50. http://geodesic.mathdoc.fr/item/VYURU_2013_6_3_a3/