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Stochastic Realization Theory in Continuous Time

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Linear Stochastic Systems

Part of the book series: Series in Contemporary Mathematics ((SCMA,volume 1))

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Abstract

This chapter is devoted to continuous-time versions of the basic results in Chaps. 6, 8 and 9 In this context, the linear stochastic model (6.1) corresponds to a system

$$\displaystyle{ \left \{\begin{array}{@{}l@{\quad }l@{}} dx = Axdt + Bdw\quad \\ dy = Cxdt + Ddw\quad \end{array} \right. }$$

of stochastic differential equations driven by the increments of a vector Wiener process w. The state process x will still be a stationary process, but the output process y has stationary increments. In the case when D = 0, we may instead consider a model

$$\displaystyle{ \left \{\begin{array}{@{}l@{\quad }l@{}} dx = Axdt + Bdw\quad \\ \phantom{d}y = Cx\quad \end{array} \right. }$$

for which the output is a stationary process.

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Authors and Affiliations

  1. Departments of Automation and Mathematics, Shanghai Jiaotong University, Shanghai, China

    Anders Lindquist

  2. Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden

    Anders Lindquist

  3. Department of Information Engineering, University of Padova, Padova, Italy

    Giorgio Picci

Authors
  1. Anders Lindquist
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  2. Giorgio Picci
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Lindquist, A., Picci, G. (2015). Stochastic Realization Theory in Continuous Time. In: Linear Stochastic Systems. Series in Contemporary Mathematics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45750-4_10

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