تقرير
Continuous-time multi-type Ehrenfest model and related Ornstein-Uhlenbeck diffusion on a star graph
| العنوان: | Continuous-time multi-type Ehrenfest model and related Ornstein-Uhlenbeck diffusion on a star graph |
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| المؤلفون: | Di Crescenzo, Antonio, Martinucci, Barbara, Spina, Serena |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Probability |
| الوصف: | We deal with a continuous-time Ehrenfest model defined over an extended star graph, defined as a lattice formed by the integers of $d$ semiaxis joined at the origin. The dynamics on each ray are regulated by linear transition rates, whereas the switching among rays at the origin occurs according to a general stochastic matrix. We perform a detailed investigation of the transient and asymptotic behavior of this process. We also obtain a diffusive approximation of the considered model, which leads to an Ornstein-Uhlenbeck diffusion process over a domain formed by semiaxis joined at the origin, named spider. We show that the approximating process possesses a truncated Gaussian stationary density. Finally, the goodness of the approximation is discussed through comparison of stationary distributions, means and variances. Comment: 30 pages, 9 figures, 3 tables, to be published in "Mathematical Methods in the Applied Sciences" |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1002/mma.8123 |
| URL الوصول: | http://arxiv.org/abs/2201.03977 |
| رقم الأكسشن: | edsarx.2201.03977 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1002/mma.8123 |
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