Dynamics under the influence of semi-Markov noise

Chvosta, Petr; Reineker, P.

doi:10.1016/s0378-4371(99)00021-7

Cited by 19 publications

(28 citation statements)

References 43 publications

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“…Several different ways to derive the corresponding equations are known in the literature (e.g., [13][14][15][16][17] ); the one especially fitted to describing response to time-dependent fields is given in [18]. For the sake of completeness, we give here the sketch of this derivation.…”

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confidence: 99%

Field-Induced Dispersion in Subdiffusion

2006

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confidence: 99%

Field-Induced Dispersion in Subdiffusion

2006

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“…Both the ATA and FATA generate exact realizations of the stochastic process. Their connection to perturbative solutions of the underlying master equation may allow one to include in future work also non-Markovian features of a stochastic dynamics by letting the rejection probabilities to depend on the history [13]. Compared to the RTA and FRTA, the new algorithms should in particular be favorable, when considering periodically driven systems with interactions.…”

Section: Discussionmentioning

confidence: 99%

“…Inserting I = D −1 D after each matrixÃ, one arrives at (13) resembles the ATA: The transition probabilities G ij (t, t ′ ) are decomposed into paths with an arbitrary number n = 0, 1, 2, . .…”

Section: Algorithmsmentioning

confidence: 99%

Attempt time Monte Carlo: An alternative for simulation of stochastic jump processes with time-dependent transition rates

Holubec

Chvosta

Einax

et al. 2011

EPL

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We present a new method for simulating Markovian jump processes with time-dependent transitions rates, which avoids the transformation of random numbers by inverting time integrals over the rates. It relies on constructing a sequence of random time points from a homogeneous Poisson process, where the system under investigation attempts to change its state with certain probabilities. With respect to the underlying master equation the method corresponds to an exact formal solution in terms of a Dyson series. Different algorithms can be derived from the method and their power is demonstrated for a set of interacting two-level systems that are periodically driven by an external field.

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“…When the channel is not memoryless, our approach also assumes additive Markov noise; other noise models are possible, for example semiMarkov noise (e.g. Chvosta and Reineker, 1999), or nonadditive noise. The approach is able to model intersymbol interference (ISI), as explained in Ferrari et al (2005).…”

Section: Discussionmentioning

confidence: 99%

Image-model coupling: a simple information theoretic perspective for image sequences

Smith

Mitchell

Budd

2009

Nonlin. Processes Geophys.

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Abstract. Images are widely used to visualise physical processes. Models may be developed which attempt to replicate those processes and their effects. The technique of coupling model output to images, which is here called "imagemodel coupling", may be used to help understand the underlying physical processes, and better understand the limitations of the models. An information theoretic framework is presented for image-model coupling in the context of communication along a discrete channel. The physical process may be regarded as a transmitter of images and the model as part of a receiver which decodes or recognises those images. Image-model coupling may therefore be interpreted as image recognition. Of interest are physical processes which exhibit "memory". The response of such a system is not only dependent on the current values of driver variables, but also on the recent history of drivers and/or system description. Examples of such systems in geophysics include the ionosphere and Earth's climate. The discrete channel model is used to help derive expressions for matching images and model output, and help analyse the coupling.

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Dynamics under the influence of semi-Markov noise

Cited by 19 publications

References 43 publications

Field-Induced Dispersion in Subdiffusion

Field-Induced Dispersion in Subdiffusion

Attempt time Monte Carlo: An alternative for simulation of stochastic jump processes with time-dependent transition rates

Image-model coupling: a simple information theoretic perspective for image sequences

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