Communications in Information and Systems

Volume 5 (2005)

Number 4

Some Markovian Properties of Linear Differential Systems

Pages: 423 – 432



C. P. Kwong

Jiangfeng Zhang


In this paper we study the Markovian properties of a system of linear partial differential equations with constant coefficients as initiated by J.C. Willems. In particular, we prove that his conjecture on Markovianity is true if the characteristic variety of the system has dimension zero. For the case when the system is defined by a differential operator, we give conditions under which the conjecture is also valid.


Linear differential systems; Markovianity; characteristic variety

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