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• W1975014929 abstract "Let {x t :t≧0} be the solution of a stochastic differential equation (SDE) in ℝ d which fixes 0, and let λ denote the Lyapunov exponent for the linear SDE obtained by linearizing the original SDE at 0. It is known that, under appropriate conditions, the sign of λ controls the stability/instability of 0 and the transience/recurrence of {x t :t≧0} on ℝ d {0}. In particular if the coefficients in the SDE depend on some parameterz which is varied in such a way that the corresponding Lyapunov exponentλ z changes sign from negative to positive the (almost-surely) stable fixed point at 0 is replaced by an (almost-surely) unstable fixed point at 0 together with an attracting invariant probability measureμ z on ℝ d {0}. In this paper we investigate the limiting behavior ofμ z asλ z converges to 0 from above. The main result is that the rescaled measures (1/λ z )μ z converge (in an appropriate weak sense) to a non-trivial σ-finite measure on ℝ d {0}." @default.
• W1975014929 created "2016-06-24" @default.
• W1975014929 creator A5077493453 @default.
• W1975014929 date "1994-12-01" @default.
• W1975014929 modified "2023-10-18" @default.
• W1975014929 title "A stochastic Hopf bifurcation" @default.
• W1975014929 cites W1979011691 @default.
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• W1975014929 doi "https://doi.org/10.1007/bf01206233" @default.
• W1975014929 hasPublicationYear "1994" @default.
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