Resonances for a diffusion with small noise

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We study resonances for the generator of a diffusion with small noise in $R^d$ :$ L_ε= -εΔ+ \nabla F \cdot \nabla$, when the potential F grows slowly at infinity (typically as a square root of the norm). The case when F grows fast is well known, and under suitable conditions one can show that there exists a family of exponentially small eigenvalues, related to the wells of F . We show that, for an F with a slow growth, the spectrum is R+, but we can find a family of resonances whose real parts behave as the eigenvalues of the "quick growth" case, and whose imaginary parts are small.
36 p

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Spectral Theory, Probability

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http://salesiana.dossiersoluciones.com/handle/123456789/212447

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0805.0106
 http://arxiv.org/abs/0805.0106

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arXiv