Statistical characteristics of the magnitude and location of the greatest maximum of Markov random process with piecewise constant drift and diffusion coefficients

Chernoyarov, Oleg V.; Salnikova, Alexandra V.; Rozanov, A.E.; Marcokova, Mariana

doi:10.12988/ams.2014.49740

Cited by 9 publications

(17 citation statements)

References 7 publications

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“…According to Eq. (18), the random process is Markov one with drift and diffusion coefficients    Therefore, we can write down [7,8] …”

Section: Duration Adaptation Algorithmmentioning

confidence: 99%

“…Here is a solution of the direct Fokker-PlanckKolmogorov equation [7][8][9]  with boundary conditions and starting condition  Applying a reflection method with sign inversion, we find the solution of Eq. (22) with coefficients (20) separately for the cases and , as it is described in [7].…”

Section: mentioning

confidence: 99%

“…(22) with coefficients (20) separately for the cases and , as it is described in [7]. Further, following [8] and substituting the found solutions in Eq. (21) we obtain expressions for false-alarm and missing probabilities in the form of  (24) Comparing Eqs.…”

Section: mentioning

confidence: 99%

“…Markovian properties of the process (33) allow finding the auxiliary function  through which the missing probability can be easily expressed [8] Here is the probability density of the random value (33). By solving this equation, as it is described in [8], we find the function (35), which we substitute in Eq.…”

Section:  mentioning

confidence: 99%

“…By solving this equation, as it is described in [8], we find the function (35), which we substitute in Eq. (36) and obtain the asymptotic expression for the missing probability in the form of …”

Section:  mentioning

confidence: 99%

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et al. 2015

Proceedings of the 2015 International Conference on Modeling, Simulation and Applied Mathematics

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“…According to Eq. (18), the random process is Markov one with drift and diffusion coefficients    Therefore, we can write down [7,8] …”

Section: Duration Adaptation Algorithmmentioning

confidence: 99%