CIR bridge for modeling of fish migration on sub-hourly scale
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909705011462144 |
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| author | Yoshioka, Hidekazu |
| author_facet | Yoshioka, Hidekazu |
| contents | Bridges, which are stochastic processes with pinned initial and terminal conditions, have recently been applied to various problems. We show that a bridge based on the Cox-Ingersoll-Ross process, called a CIR bridge in this paper, reasonably models the intraday number of migrating fish at an observation point in a river. The studied fish migrates between sunrise and sunset each day, which are considered the initial and terminal times, respectively. The CIR bridge is well-defined as a unique pathwise continuous solution to a stochastic differential equation with unbounded drift and diffusion coefficients and potentially represents the on-off intermittency of the fish count data. Our bridge is theoretically novel in that it admits closed-form time-dependent averages and variances, with which the model parameters can be identified efficiently, and is computable by a recently-developed one-step numerical method. The CIR bridge is applied to the sub-hourly migration data of the diadromous fish Plecoglossus altivelis altivelis in the Nagara River, Japan, from February to June. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | CIR bridge for modeling of fish migration on sub-hourly scale Yoshioka, Hidekazu Probability Numerical Analysis Bridges, which are stochastic processes with pinned initial and terminal conditions, have recently been applied to various problems. We show that a bridge based on the Cox-Ingersoll-Ross process, called a CIR bridge in this paper, reasonably models the intraday number of migrating fish at an observation point in a river. The studied fish migrates between sunrise and sunset each day, which are considered the initial and terminal times, respectively. The CIR bridge is well-defined as a unique pathwise continuous solution to a stochastic differential equation with unbounded drift and diffusion coefficients and potentially represents the on-off intermittency of the fish count data. Our bridge is theoretically novel in that it admits closed-form time-dependent averages and variances, with which the model parameters can be identified efficiently, and is computable by a recently-developed one-step numerical method. The CIR bridge is applied to the sub-hourly migration data of the diadromous fish Plecoglossus altivelis altivelis in the Nagara River, Japan, from February to June. |
| title | CIR bridge for modeling of fish migration on sub-hourly scale |
| topic | Probability Numerical Analysis |
| url | https://arxiv.org/abs/2506.07094 |