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The theory of statistical controls was first discussed by T. Kitagawa [1], [2], as contained in successive processes. In a previous paper [3], the author studied this theory in detail by defining the ...linear controlled stochastic process (l. c. s. p.) for the discrete parameter case. A l. c. s. p. is the stochastic process which is transformed from an original stochastic process by the linear control. Some concrete types of discrete parameter l. c. s. p. and the fluctuation of the control system error were given in [3]. In the analogy to the discrete parameter l. c. s. p., we shall consider the continuous parameter l. c. s. p. in this paper. The definition and covariance function of continuous parameter l. c. s. p. are given in §2 and §3 respectively. In §4 the mean square errors of continuous linear control system are considered. Some examples are given in §5 to illustrate the structure and practical applications of continuous parameter l. c. s. p.. It is to be noted that throughout this paper we are concerned with the Loeve's second order random functions, and hence that in what follows the word "stochastic process" always implies such a second order random function.show more
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