Surveys in Mathematics and its Applications

ISSN 1842-6298
 Volume 1 (2006), 117 - 134

REPRESENTATION THEOREM FOR STOCHASTIC DIFFERENTIAL EQUATIONS IN HILBERT SPACES AND ITS APPLICATIONS

Viorica Mariela Ungureanu

Abstract. In this survey we recall the results obtained in [16] where we gave a representation theorem for the solutions of stochastic differential equations in Hilbert spaces. Using this representation theorem we obtained deterministic characterizations of exponential stability and uniform observability in [16], [17] and we will prove a result of Datko type concerning the exponential dichotomy of stochastic equations.

2000 Mathematics Subject Classification: 53C26, 53C12, 51H25.
Keywords: Lyapunov equations, stochastic differential equations, uniform exponential stability, uniform observability, uniform exponential dichotomy

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Acknowledgement. This work was supported by the CEEX grant PR-D11-PT00-48/2005, contract no 69/2006, from the Romanian Ministry of Education and Research.

Viorica Mariela Ungureanu
University Constantin Brâncuşi of Târgu-Jiu,
Bld. Republicii 1, 210152, Târgu-Jiu,
Romania.
e-mail: vio@utgjiu.ro
http://www.utgjiu.ro/math/vungureanu/

http://www.utgjiu.ro/math/sma