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CIR bridge for modeling of fish migration on sub-hourly scale

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  • Yoshioka, Hidekazu

Abstract

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.

Suggested Citation

  • Yoshioka, Hidekazu, 2025. "CIR bridge for modeling of fish migration on sub-hourly scale," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    • Handle: RePEc:eee:chsofr:v:199:y:2025:i:p3:s0960077925008872
    DOI: 10.1016/j.chaos.2025.116874
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