Evolution of moments and correlations in non-renewal escape-time processes
The theoretical description of non-renewal stochastic systems is a challenge. Analytical results are often not available or can only be obtained under strong conditions, limiting their applicability. Also, numerical results have mostly been obtained by ad-hoc Monte--Carlo simulations, which are usua...
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| Format: | Article |
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American Physical Society
2017
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| Online Access: | https://eprints.nottingham.ac.uk/42745/ |
| _version_ | 1848796557856473088 |
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| author | Braun, Wilhelm Thul, Ruediger Longtin, André |
| author_facet | Braun, Wilhelm Thul, Ruediger Longtin, André |
| author_sort | Braun, Wilhelm |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | The theoretical description of non-renewal stochastic systems is a challenge. Analytical results are often not available or can only be obtained under strong conditions, limiting their applicability. Also, numerical results have mostly been obtained by ad-hoc Monte--Carlo simulations, which are usually computationally expensive when a high degree of accuracy is needed. To gain quantitative insight into these systems under general conditions, we here introduce a numerical iterated first-passage time approach based on solving the time-dependent Fokker--Planck equation (FPE) to describe the statistics of non-renewal stochastic systems. We illustrate the approach using spike-triggered neuronal adaptation in the leaky and perfect integrate-and-fire model, respectively. The transition to stationarity of first-passage time moments and their sequential correlations occur on a non-trivial timescale that depends on all system parameters. Surprisingly this is so for both single exponential and scale-free power-law adaptation. The method works beyond the small noise and timescale separation approximations. It shows excellent agreement with direct Monte Carlo simulations, which allows for the computation of transient and stationary distributions. We compare different methods to compute the evolution of the moments and serial correlation coefficients (SCC), and discuss the challenge of reliably computing the SCC which we find to be very sensitive to numerical inaccuracies for both the leaky and perfect integrate-and-fire models. In conclusion, our methods provide a general picture of non-renewal dynamics in a wide range of stochastic systems exhibiting short and long-range correlations. |
| first_indexed | 2025-11-14T19:49:53Z |
| format | Article |
| id | nottingham-42745 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:49:53Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-427452020-05-04T18:45:42Z https://eprints.nottingham.ac.uk/42745/ Evolution of moments and correlations in non-renewal escape-time processes Braun, Wilhelm Thul, Ruediger Longtin, André The theoretical description of non-renewal stochastic systems is a challenge. Analytical results are often not available or can only be obtained under strong conditions, limiting their applicability. Also, numerical results have mostly been obtained by ad-hoc Monte--Carlo simulations, which are usually computationally expensive when a high degree of accuracy is needed. To gain quantitative insight into these systems under general conditions, we here introduce a numerical iterated first-passage time approach based on solving the time-dependent Fokker--Planck equation (FPE) to describe the statistics of non-renewal stochastic systems. We illustrate the approach using spike-triggered neuronal adaptation in the leaky and perfect integrate-and-fire model, respectively. The transition to stationarity of first-passage time moments and their sequential correlations occur on a non-trivial timescale that depends on all system parameters. Surprisingly this is so for both single exponential and scale-free power-law adaptation. The method works beyond the small noise and timescale separation approximations. It shows excellent agreement with direct Monte Carlo simulations, which allows for the computation of transient and stationary distributions. We compare different methods to compute the evolution of the moments and serial correlation coefficients (SCC), and discuss the challenge of reliably computing the SCC which we find to be very sensitive to numerical inaccuracies for both the leaky and perfect integrate-and-fire models. In conclusion, our methods provide a general picture of non-renewal dynamics in a wide range of stochastic systems exhibiting short and long-range correlations. American Physical Society 2017-05-16 Article PeerReviewed Braun, Wilhelm, Thul, Ruediger and Longtin, André (2017) Evolution of moments and correlations in non-renewal escape-time processes. Physical Review E, 95 . 052127. ISSN 1550-2376 https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.052127 doi:10.1103/PhysRevE.95.052127 doi:10.1103/PhysRevE.95.052127 |
| spellingShingle | Braun, Wilhelm Thul, Ruediger Longtin, André Evolution of moments and correlations in non-renewal escape-time processes |
| title | Evolution of moments and correlations in non-renewal escape-time processes |
| title_full | Evolution of moments and correlations in non-renewal escape-time processes |
| title_fullStr | Evolution of moments and correlations in non-renewal escape-time processes |
| title_full_unstemmed | Evolution of moments and correlations in non-renewal escape-time processes |
| title_short | Evolution of moments and correlations in non-renewal escape-time processes |
| title_sort | evolution of moments and correlations in non-renewal escape-time processes |
| url | https://eprints.nottingham.ac.uk/42745/ https://eprints.nottingham.ac.uk/42745/ https://eprints.nottingham.ac.uk/42745/ |