We study infinite-dimensional stochastic port-Hamiltonian systems (SPHSs) having multiplicative and boundary input noise. Using Itô and Stratonovich integrals on Hilbert spaces, a formal mathematical description of this specific class of stochastic systems is presented, and some properties, including almost sure and weak passivity, are investigated. By considering dissipative effects, we derive a condition for SPHSs to be weakly passive. Finally, the stochastic port-Hamiltonian framework and the passivity concepts are illustrated on the example of an inhomogeneous vibrating string subject to random damping and state noises.

中文翻译：

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受乘法和输入噪声影响的边界控制和观测随机哈密尔顿系统的无源性

我们研究具有乘法和边界输入噪声的无限维随机哈密顿系统 (SPHS)。使用希尔伯特空间上的 Itô 和 Stratonovich 积分，给出了这类特定随机系统的正式数学描述，并研究了一些性质，包括几乎肯定和弱被动性。通过考虑耗散效应，我们推导出了 SPHS 弱被动的条件。最后，以受随机阻尼和状态噪声影响的非均匀振动弦为例说明了随机哈密尔顿框架和无源性概念。