Lyapunov Exponent and Rotation Number of Two-Dimensional Linear Stochastic Systems with Small Diffusion
Abstract
By means of a singular perturbation scheme and large deviation estimates we expand the Lyapunov exponent and rotation number in terms of the (small) noise intensity $\varepsilon $ for all $2 \times 2$ systems $dX_t^\varepsilon = AX_t^\varepsilon dt + \sqrt \varepsilon \sum\nolimits_{k = 1}^r {B_k } X_t^\varepsilon \circ dW_t^k $ for which A is complex diagonalizable. Examples are given.
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Copyright © 1988 Society for Industrial and Applied Mathematics.
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Submitted: 16 July 1986
Accepted: 9 March 1987
Published online: 10 July 2006
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