Geodesic
Maslov idempotent probability calculus,~I
Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 4, pp. 735-751

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

Maslov's idempotent measures allow an optimization theory to be derived at the same level of generality as probability and stochastic process theory. One purpose of this work is to present the basic concepts of this $(\max,+)$-version of probability theory. Using this framework we will see that the Bellman optimality principle is the idempotent version of the classical Markov causality principle. Applications to optimal control problems, Hamilton–Jacobi equations, and mathematical morphology are discussed in the second part of this study.
Keywords: optimization theory, Maslov idempotent measure, idempotent probability calculus, Bellman–Markov processes. 
@article{TVP_1998_43_4_a5,
     author = {P. Del Moral and M. Doisy},
     title = {Maslov idempotent probability {calculus,~I}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {735--751},
     publisher = {mathdoc},
     volume = {43},
     number = {4},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_1998_43_4_a5/}
}
TY  - JOUR
AU  - P. Del Moral
AU  - M. Doisy
TI  - Maslov idempotent probability calculus,~I
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1998
SP  - 735
EP  - 751
VL  - 43
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_1998_43_4_a5/
LA  - en
ID  - TVP_1998_43_4_a5
ER  - 
%0 Journal Article
%A P. Del Moral
%A M. Doisy
%T Maslov idempotent probability calculus,~I
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1998
%P 735-751
%V 43
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1998_43_4_a5/
%G en
%F TVP_1998_43_4_a5
P. Del Moral; M. Doisy. Maslov idempotent probability calculus,~I. Teoriâ veroâtnostej i ee primeneniâ, Tome 43 (1998) no. 4, pp. 735-751. http://geodesic.mathdoc.fr/item/TVP_1998_43_4_a5/