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We present theoretical foundations of stability analysis for attractors of stochastically forced nonlinear systems. Our technique is based on extension of Lyapunov function technique to general manifolds. The first approximation stochastic linear systems for attractors are introduced and a notion of projective stability is proposed. A general criterion for projective stability is obtained. We propose a constructive approach to stochastic stability investigation of limit cycles and tori based on spectral analysis. The stochastic stability analysis is reduced to the estimation of the spectral radius of some positive operator. The possibilities of this approach are demonstrated for important cases of limit cycle on a plane and 2-torus. For these cases, the explicit parametrical criteria are found. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

We study the emission of gravitational waves by EMRIs in numerically produced spacetimes which are highly accurate solutions of Einstein equations and contain a black hole and a torus. In order to assess the maximal impact these tori could have on the produced waveforms, we consider them as compact, massive and close to the central black hole and try to determine whether LISA can detect their presence. Our results reinforce the confusion problem recently pointed out in [1]. © 2006 American Institute of Physics [ABSTRACT FROM AUTHOR]