Well-posedness of Stochastic Port-Hamiltonian Systems on Infinite-dimensional Spaces

François Lamoline; Joseph J. Winkin

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arXiv · 1907.04158

Well-posedness of Stochastic Port-Hamiltonian Systems on Infinite-dimensional Spaces

François Lamoline·Joseph J. Winkin

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Abstract

Stochastic port-Hamiltonian systems on infinite-dimensional spaces governed by It\^o stochastic differential equations (SDEs) are introduced and some properties of this new class of systems are studied. They are an extension of stochastic port-Hamiltonian systems defined on a finite-dimensional state space. The concept of well-posedness in the sense of Weiss and Salamon is generalized to the stochastic context. Under this extended definition, stochastic port-Hamiltonian systems are shown to be well-posed. The theory is illustrated on an example of a vibrating string subject to a Hilbert space-valued Gaussian white noise process.

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BibTeX RIS

François Lamoline, Joseph J. Winkin. 2019-07-09. Well-posedness of Stochastic Port-Hamiltonian Systems on Infinite-dimensional Spaces. https://arxiv.org/abs/1907.04158

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