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<p>This paper focuses on a stochastic four-species food chain model incorporating the Ornstein-Uhlenbeck process. First, we establish the existence and uniqueness of the global solution for the model. Then, we derive sufficient conditions for the existence of the stationary distribution for the model by constructing suitable Lyapunov functions. Next, we derive the explicit expression of the probability density function (PDF) for the model in the vicinity of its quasi-equilibrium. Finally, some numerical examples are provided to verify the theoretical results.</p>

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Stationary Distribution and Density Function of a Stochastic Population Model with Ornstein-Uhlenbeck Process

  • 期刊论文

  • 发表日期：

    2026年5月19日

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  • Sheng Wang,
  • Zeyan Yue,
  • Jiarui Meng

摘要

This paper focuses on a stochastic four-species food chain model incorporating the Ornstein-Uhlenbeck process. First, we establish the existence and uniqueness of the global solution for the model. Then, we derive sufficient conditions for the existence of the stationary distribution for the model by constructing suitable Lyapunov functions. Next, we derive the explicit expression of the probability density function (PDF) for the model in the vicinity of its quasi-equilibrium. Finally, some numerical examples are provided to verify the theoretical results.