Characterization and Classification of Gaussian Second Order Reciprocal Processes
Continuous time second order reciprocal processes were introduced in 1979 by R. N. Miroshin . A mean square differentiable process x(t) is second order reciprocal if the process constructed stacking in a vector x(t) and its mean square derivative x’(t) has the reciprocal property. In this paper we show that, under suitable assumptions, one can characterize Gaussian second order reciprocal processes in terms of fourth order linear stochastic differential equations driven by locally correlated noise and with boundary value conditions. Then, we use this characterization to repeat the classification of Gaussian, scalar, stationary second order reciprocal processes already done by Carmichael, Masse’ and Theodorescu .
KeywordsStochastic Differential Equation Conjugate Point Side Constraint Schwartz Inequality Residual Process
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