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In recent works, a new approach to discrete-time linear stochastic systems was developed, using Hida’s white noise space theory and the related theory of stochastic distributions. In the present work, we study continuous-time linear systems using the above approach. This involves subtleties not present in the discrete case. We focus in particular on the state space equations of linear continuous stochastic systems where the coefficients are matrices with entries in a certain commutative algebra, and on the associated transfer function. We then consider the case of systems given in descriptor form.

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Continuous Stochastic Linear Systems: A White Noise Space Approach

  • 会议论文

  • 发表日期：

    2026年

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  • Daniel Alpay,
  • Alon Bublil

摘要

In recent works, a new approach to discrete-time linear stochastic systems was developed, using Hida’s white noise space theory and the related theory of stochastic distributions. In the present work, we study continuous-time linear systems using the above approach. This involves subtleties not present in the discrete case. We focus in particular on the state space equations of linear continuous stochastic systems where the coefficients are matrices with entries in a certain commutative algebra, and on the associated transfer function. We then consider the case of systems given in descriptor form.