The asymptotic behaviors of the principal eigenvalue and the
corresponding normalized eigenfunction of the operator $G^\varepsilon f =
(\varepsilon/2)\triangle f + g \triangledown f +(l/\varepsilon)f$ for small
$\varepsilon$ are studied. Under some conditions, the first order expansions
for them are obtained. Two applications to risk-sensitive control problems are
also mentioned.
Publié le : 1997-10-14
Classification:
Diffusion processes with small noise,
first eigenvalue and eigenfunction,
discounted control problem,
viscosity solution,
large deviations,
risk sensitive control,
Primary 60H30,
93B36,
93E20
@article{1023481117,
author = {Fleming, Wendell H. and Sheu, Shuenn-Jyi},
title = {Asymptotics for the principal eigenvalue and eigenfunction of a
nearly first-order operator with large potential},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 1953-1994},
language = {en},
url = {http://dml.mathdoc.fr/item/1023481117}
}
Fleming, Wendell H.; Sheu, Shuenn-Jyi. Asymptotics for the principal eigenvalue and eigenfunction of a
nearly first-order operator with large potential. Ann. Probab., Tome 25 (1997) no. 4, pp. 1953-1994. http://gdmltest.u-ga.fr/item/1023481117/