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Article Dans Une Revue IMA Journal of Mathematical Control and Information Année : 2012

A note on the controllability of jump diffusions with linear coefficients

Dan Goreac
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Résumé

We investigate the approximate controllability property for a class of linear stochastic equations driven by independent Brownian motion and Poisson random measure. The paper generalizes recent results of Buckdahn et al. (2006, A characterization of approximately controllable linear stochastic differential equations. Stochastic Partial Differential Equations and Applications (G. Da Prato & L. Tubaro eds). Series of Lecture Notes in Pure and Applied Mathematics, vol. 245. London: Chapman & Hall, pp. 253-260) and Goreac (2008, A Kalman-type condition for stochastic approximate controllability. C. R. Math. Acad. Sci. Paris, 346, 183-188; 2009, Approximate controllability for linear stochastic differential equations in infinite dimensions. Appl. Math. Optim., 60, 105-132). An equivalent conditional invariance criterion is given. In general, this (explicit) criterion involves an 핃2-space, but, for particular cases, an iterative finite scheme is provided.
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Dates et versions

hal-00728378 , version 1 (05-09-2012)

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Dan Goreac. A note on the controllability of jump diffusions with linear coefficients. IMA Journal of Mathematical Control and Information, 2012, 29 (3), pp.427-435. ⟨10.1093/imamci/dns001⟩. ⟨hal-00728378⟩
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