Scholarlink

<p>We introduce an abstract Hilbert space-valued framework of Markovian lifts for stochastic Volterra equations with operator-valued Volterra kernels. Our main results address the existence and characterisation of possibly multiple limit distributions and stationary processes, a law of large numbers including a convergence rate, and the central limit theorem for time averages of the process within the Gaussian domain of attraction. As particular examples, we study Markovian lifts based on Laplace transforms in a weighted Hilbert space of densities and Markovian lifts based on the shift semigroup on the Filipović space. We illustrate our results for the case of fractional stochastic Volterra equations with additive or multiplicative Gaussian noise.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Limit theorems for stochastic Volterra processes

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月18日

查看全文
  • Luigi Amedeo Bianchi,
  • Stefano Bonaccorsi,
  • Ole Cañadas,
  • Martin Friesen

摘要

We introduce an abstract Hilbert space-valued framework of Markovian lifts for stochastic Volterra equations with operator-valued Volterra kernels. Our main results address the existence and characterisation of possibly multiple limit distributions and stationary processes, a law of large numbers including a convergence rate, and the central limit theorem for time averages of the process within the Gaussian domain of attraction. As particular examples, we study Markovian lifts based on Laplace transforms in a weighted Hilbert space of densities and Markovian lifts based on the shift semigroup on the Filipović space. We illustrate our results for the case of fractional stochastic Volterra equations with additive or multiplicative Gaussian noise.