The probability of wrongdecisions in the estimation of states of a generalized semi-synchronous flow of events.

Generalized semi-synchronous flow of events which intensity is piecewise constant stochasticprocess ƒ(t) with two states ƒ1 and ƒ2 (ƒ1 > ƒ2) is considered. During the time interval whenƒ(t) = ƒi , Poisson flow of events takes place with the intensity ƒi, i = 1,2. Transition from the firststate of the process ƒ(t) into the second one is possible only at the moment of event occurrence,thus, the transition is carried out with probability p (0 < p ≤ 1); with probability 1 - p process ƒ(t)remains in the first state. In this case the duration of process stay ƒ(t) in the first state is a randomvariable with exponential distribution function 1F1(ƒ) =1−e− pƒ ƒ . Transition from the second stateof process into the first state can be carried out at any moment of time. Thus, duration of processstay ƒ(t) in the second condition is distributed in accordance with the exponential law:F2(ƒ) =1−e−ƒƒ . The process of transition ƒ(t) from the second state into the first initiates withprobability ƒ (0 ≤ ƒ ≤ 1) additional event in the first 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 Po(w(ƒ1|ti + 0),ƒi) at any time ƒi ≥ 0, i = 0,1… (general case) is proposed. For the particular and special cases ofrelations between flow parameters the unconditional probability of wrong decision is found.

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