Lyapunov exponent and rotation number of 2-dimensional linear stochastic-systems with telegraphic noise Export

@article{LoparoF93, abstract = {In this paper, the Lyapunov exponent and rotation number of a family of two-dimensional systems with general telegraphic noise where the unperturbed system has oscillatory behavior are studied. Using a martingale approach, an iterative computational procedure is derived and analytic expansions in the noise strength are obtained for the Lyapunov exponent and the rotation number. These expansions are convergent in a nonmarginal way. The positivity of the exponent is also established for the random harmonic oscillator with zero-mean telegraphic noise, and lower and upper bounds are derived for the exponent when the noise is the random telegraph process.}, author = {Loparo, K. A. and Feng, X. B.}, citeulike-article-id = {1597120}, journal = {Siam Journal On Applied Mathematics}, keywords = {exponents, le, lyapunov, noise}, pages = {283--300}, posted-at = {2007-08-27 18:58:07}, priority = {2}, title = {Lyapunov exponent and rotation number of 2-dimensional linear stochastic-systems with telegraphic noise}, volume = {53}, year = {1993} }

TY - JOUR ID - LoparoF93 L3 - citeulike-article-id:1597120 N2 - In this paper, the Lyapunov exponent and rotation number of a family of two-dimensional systems with general telegraphic noise where the unperturbed system has oscillatory behavior are studied. Using a martingale approach, an iterative computational procedure is derived and analytic expansions in the noise strength are obtained for the Lyapunov exponent and the rotation number. These expansions are convergent in a nonmarginal way. The positivity of the exponent is also established for the random harmonic oscillator with zero-mean telegraphic noise, and lower and upper bounds are derived for the exponent when the noise is the random telegraph process. JF - Siam Journal On Applied Mathematics EP - 300 TI - Lyapunov exponent and rotation number of 2-dimensional linear stochastic-systems with telegraphic noise VL - 53 SP - 283 KW - exponents KW - le KW - lyapunov KW - noise AU - Loparo, KA AU - Feng, XB PY - 1993/// ER -