Characterising non-renewal stochastic dynamics by an iterated first-passage time approach
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1
University of Ottawa, Department of Physics, Canada
We explain how to compute stationary distributions in two-dimensional stochastic systems where one variable evolves as a diffusion process, and the other variable evolves deterministically and suffers finite jumps at random times specified by the first passage time of the diffusion variable to a constant threshold. Our approach, working beyond the small noise and timescale separation approximations, makes use of standard finite-element discretisation techniques and requires only boundary conditions that are easy to implement. Our results provide a practical way to compute stationary distributions in a wide range of non-renewal stochastic systems exhibiting long-range dependencies and serial correlations, such as neuron models for spike-frequency adaptation and for decision making.
Keywords:
non-renewal process,
spike-triggered adaptation,
stochastic processes,
neuron model,
serial correlation,
long range dependence
Conference:
Neuroinformatics 2016, Reading, United Kingdom, 3 Sep - 4 Sep, 2016.
Presentation Type:
Poster
Topic:
Computational neuroscience
Citation:
Braun
W and
Longtin
A
(2016). Characterising non-renewal stochastic dynamics by an iterated first-passage time approach.
Front. Neuroinform.
Conference Abstract:
Neuroinformatics 2016.
doi: 10.3389/conf.fninf.2016.20.00070
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Received:
27 May 2016;
Published Online:
18 Jul 2016.
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Correspondence:
Dr. Wilhelm Braun, University of Ottawa, Department of Physics, Ottawa, Ontario, K1N6N5, Canada, wbraun@uottawa.ca