Forcing a Stochastic Process to Stay in or to Leave a Given Region
Lefebvre, Mario
Ann. Appl. Probab., Tome 1 (1991) no. 4, p. 167-172 / Harvested from Project Euclid
Systems defined by $dx(t) = a\lbrack x(t), t \rbrack dt + B\lbrack x(t), t \rbrack u(t) dt + N^{1/2}\lbrack x(t), t \rbrack dW(t)$, where $x(t)$ is the state variable, $u(t)$ is the control variable, $a$ is a vector function, $B$ and $N$ are matrices and $W(t)$ is a Brownian motion process, are considered. The aim is to minimize the expected value of a cost function with quadratic control costs on the way and terminal cost function $K(T)$, where $T = \inf\{s: x(s) \in D \mid x(t) = x\}, D$ being a given region in $\mathbb{R}^n$. The function $K$ is taken to be 0 if $T \geq (\leq) \tau$, where $\tau$ is a positive constant and $+\infty$ if $T < (>) \tau$ when the aim is to force $x(t)$ to stay in (resp., to leave) the region $C$, the complement of $D$. A particular one-dimensional problem is solved explicitly and a risk-sensitive version of the general problem is also considered.
Publié le : 1991-02-14
Classification:  Stochastic control,  optimal control,  Brownian motion,  risk sensitivity,  93E20,  60J70
@article{1177005986,
     author = {Lefebvre, Mario},
     title = {Forcing a Stochastic Process to Stay in or to Leave a Given Region},
     journal = {Ann. Appl. Probab.},
     volume = {1},
     number = {4},
     year = {1991},
     pages = { 167-172},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177005986}
}
Lefebvre, Mario. Forcing a Stochastic Process to Stay in or to Leave a Given Region. Ann. Appl. Probab., Tome 1 (1991) no. 4, pp.  167-172. http://gdmltest.u-ga.fr/item/1177005986/