Linear stochastic state space theory in the white noise space setting

Daniel Alpay, David Levanony, Ariel Pinhas

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We study linear stochastic state space equations within the white noise space setting. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this commutative ring and are characterized in a number of ways. A major feature in our approach is the observation that key characteristics of a linear, time invariant, stochastic system are determined by the corresponding characteristics associated with the deterministic part of the system, namely, its average behavior.

Original languageEnglish
Pages (from-to)5009-5027
Number of pages19
JournalSIAM Journal on Control and Optimization
Issue number8
StatePublished - 1 Dec 2010


  • Random systems
  • State space equations
  • Systems over commutative rings
  • White noise space
  • Wick product

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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