On Conditional Markov Processes
Copyright policy )On Conditional Markov Processes
In this paper a pair of random processes $X_t $, $Y_t $, which conjunctly form the Markov process $Z_t $ is considered. The conditional distribution of the process $Y_t $ for the condition of a known realization of the process $X_t $ during some time interval is examined. E. B. Dynkin has proposed that if $X_t $ is a Markov process, the conditional distribution of $Y_t $ will satisfy a functional equation similar to the known Kolmogorov-Chapman equation. The author has proved this proposition, but details of the proof are omitted here.
probability theory, Markov processes, probability theory etc., Probability theory and stochastic processes
probability theory, Markov processes, probability theory etc., Probability theory and stochastic processes
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