Journal Article

A note on the controllability of jump diffusions with linear coefficients

Dan Goreac

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 29, issue 3, pages 427-435
Published in print September 2012 | ISSN: 0265-0754
Published online February 2012 | e-ISSN: 1471-6887 | DOI:
A note on the controllability of jump diffusions with linear coefficients

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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 𝕃2-space, but, for particular cases, an iterative finite scheme is provided.

Keywords: controllability; stochastic differential equation; jump diffusion; riccati equation

Journal Article.  0 words. 

Subjects: Mathematics

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