Вероятность ошибки при оценивании состояний обобщенного асинхронного потока событий

Generalized asynchronous flow of events which intensity is piecewise constant stochastic process 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 state of process λ(t) into the second one (from the second state into the first one) is carried out at any moment 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 with probability p (0≤ p ≤1) extra event in the second state. Also the process of transition λ(t) from the second state into the first one initiates with probability вероятностью q (0≤ q ≤1) extra event in the second state. We solve the problem of finding the unconditional (or conditional) probability of error decision. The algorithm for calculating the conditional probability of wrong decisions P0(ω(λ1|ti+0), τi) at any time τi ≥ 0, i=0,1,… (general case) is proposed. For the particular and special cases of relations between flow parameters the unconditional probability of wrong decision is found.