The probability ofwrong decisions in the estimation of states of a generalized asynchronous flow of events

Generalized asynchronous flow of events which intensity is piecewise constant stochasticprocess λ(t) with two states λ1 and λ2 (λ1> λ2) is considered. During the time interval when λ(t) =λi , Poisson flow of events takes place with the intensity λi , i=1,2. Transition from the first stateof process λ(t) into the second one (from the second state into the first one) is carried out at anymoment of time. The sojourn time in the i-th state is exponentially distributed with parameter αi ,i=1,2. The process of transition λ(t) from the first state into the second one initiates withprobability p (0≤ p ≤1) extra event in the second state. Also the process of transition λ(t) from thesecond state into the first one initiates with probability вероятностью q (0≤ q ≤1) extra event inthe second state.We solve the problem of finding the unconditional (or conditional) probability of errordecision. The algorithm for calculating the conditional probability of wrong decisionsP0(ω(λ1|ti+0), τi) at any time τi ≥ 0, i=0,1,… (general case) is proposed. For the particular andspecial cases of relations between flow parameters the unconditional probability of wrongdecision is found.

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