The aim of this paper is to give two characterizations of approximate controllability of a controlled linear stochastic differential equation. The first characterization can be formulated by saying that an ad hoc backward stochastic differential equation has only one solution which is constant equal to zero. The second criterion for approximate controllability - which is the main result of the present Note - says that the only invariant (or viable) set contained in a suitable linear space is the trivial space 0. A explicit way for checking the invariance (or viability) of a linear space is provided. We emphasize that the characterization of approximate controllability is easily computable.
Buckdahn, R., Quincampoix, M., Tessitore, G. (2006). A characterization of approximately controllable linear stochastic differential equations. In G. Da Prato, L. Tubaro (a cura di), Stochastic partial differential equations and applications. VII (pp. 53-60). London : Chapman & Hall.
A characterization of approximately controllable linear stochastic differential equations
TESSITORE, GIANMARIO
2006
Abstract
The aim of this paper is to give two characterizations of approximate controllability of a controlled linear stochastic differential equation. The first characterization can be formulated by saying that an ad hoc backward stochastic differential equation has only one solution which is constant equal to zero. The second criterion for approximate controllability - which is the main result of the present Note - says that the only invariant (or viable) set contained in a suitable linear space is the trivial space 0. A explicit way for checking the invariance (or viability) of a linear space is provided. We emphasize that the characterization of approximate controllability is easily computable.
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