A finitely additive version of Poincare's recurrence theorem

Francke, H.; Plachky, Detlef; Thomsen, W.

doi:10.1007/bfb0041159

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“…This can be de®ned as var lj B R E lj B R 2 À E lj B R 2 . We use the following result (Theorem 3 of Francke et al 1985; see Blum and Rosenblatt 1967 for the original result; also Wolfowitz 1967):…”

Section: Outline Of Approachmentioning

confidence: 99%

Estimating statistics of neuronal dynamics via Markov chains

Froyland

Aihara

2001

Biol Cybern

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We present an efficient computational method for estimating the mean and variance of interspike intervals defined by the timing of spikes in typical orbits of one-dimensional neuronal maps. This is equivalent to finding the mean and variance of return times of orbits to particular regions of phase space. Rather than computing estimates directly from time series, the system is modelled as a finite state Markov chain to extract stationary behaviour in the form of invariant measures and average absorption times. Ergodic-theoretic formulae are then applied to produce the estimates without the need to generate orbits directly. The approach may be applied to both deterministic and randomly forced systems.

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Section: Outline Of Approachmentioning

confidence: 99%