ON THE SOLUTION OF KAC-TYPE PARTIAL-DIFFERENTIAL EQUATIONS

The Cauchy problem in the form of (1.11) with linear and constant coefficients is discussed. The solution (1.10) can be given in explicit form when the stochastic process is a multidimensional autoregression (AR) type, or Ornstein-Uhlenbeck process. Functionals of (1.10) form were studied by Kac in the Brownian motion case. The solutions are obtained with the help of the Radon-Nikodym transformation, proposed by Novikov [12].