Keywords: random process, probability of reaching a level, moment of first reaching the level, landing of an airplane, forecasting, control
Subject:
Mathematical modeling, theory of random processes, theory of control and decision-making and their applications.The main efforts were aimed at solving the practically important problem of finding the distribution function of the moment of the first output of a vector random process on the selected part of the boundary of a given region in multidimensional space. This problem appears in studying stochastic systems in situations when normal system operation corresponds to a position of a point depicting the system in a certain region of the systems phase space, and consequences of the point leaving this region depend on which part of the regions boundary it will leave through. The scheme is proposed that allows one to find estimates of the probability of events associated with level crossings and level achievements by a non-Markovian smooth random process. The results obtained are used, in particular, in aviation to solve the problem of ensuring the safety of aircraft flight.
Main publications:
S. L. Semakov, “The probability of hitting of a level by a component of multidimensional process within prescribed interval under restrictions on the remaining components”, Theory Probab. Appl., 34:2 (1989), 357–361
S. L. Semakov, Outliers of Random Processes: Applications in Aviation, Nauka, Moscow, 2005 , 200 pp. (in Russian)
S. L. Semakov, I. S. Semakov, “Estimating the probability that a random process first reaches the boundary of a region on a given time interval”, Proceedings of the 57th IEEE Conference on Decision and Control (CDC2018) (Miami Beach, Fl, USA, December 17–19, 2018), 2018, 256–261
S. L. Semakov, Crossings problems in random processes theory and their applications in aviation, Cambridge Scholars Publishing, Newcastle, UK, 2019 , 200 pp.
S. Semakov and I. Semakov, “Method of calculating the probability of a safe landing for ship-based aircraft”, IEEE Transactions on Aerospace and Electronic Systems, 58:6 (2022), 5425–5442
