Scholarlink

<p>We derive a Gronwall type inequality for mild solutions of non-autonomous parabolic rough partial differential equations (RPDEs).&#xa0;This inequality together with an analysis of the Cameron-Martin space associated to the noise, allows us to obtain the existence of moments of all order for the solution of the corresponding RPDE and its Jacobian when the random input is given by a Gaussian Volterra process.&#xa0;Applying further the multiplicative ergodic theorem, these integrable bounds entail the existence of Lyapunov exponents for RPDEs.&#xa0;We illustrate these results for stochastic partial differential equations with multiplicative boundary 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

A mild rough Gronwall lemma with applications to non-autonomous evolution equations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年11月2日

查看全文
  • Alexandra Blessing Neamţu,
  • Mazyar Ghani Varzaneh,
  • Tim Seitz

摘要

We derive a Gronwall type inequality for mild solutions of non-autonomous parabolic rough partial differential equations (RPDEs). This inequality together with an analysis of the Cameron-Martin space associated to the noise, allows us to obtain the existence of moments of all order for the solution of the corresponding RPDE and its Jacobian when the random input is given by a Gaussian Volterra process. Applying further the multiplicative ergodic theorem, these integrable bounds entail the existence of Lyapunov exponents for RPDEs. We illustrate these results for stochastic partial differential equations with multiplicative boundary noise.