CONDITIONED STOCHASTIC-PROCESSES FOR CONDITIONAL RANDOM-FIELDS

Analytical development is presented for the theory of conditional rand om fields involving conditioning deterministic time functions. After d iscussion of their basic concept and their engineering significance, t he probability distribution of the Fourier coefficients for conditione d stochastic processes is derived. Its physical interpretation is pres ented in terms of harmonic amplitudes and phase angles. On this basis, solutions are obtained for the time-varying mean values and the varia nces of conditioned stochastic processes as well as their first-passag e probabilities. Numerical simulation of the conditional random fields is also performed for assumed power spectral density and coherence fu nctions. These results are discussed in terms of the probability theor y and engineering application. Specifically, effects of coherency and the number of conditioning deterministic time functions are examined.