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One method of parameter estimation for the model of radioactive pollution. (Ukrainian) Zbl 0928.62117

The process \(x(t)=\sum _{i = 1}^mx_i(t)\) is considered, where \(x_i(t)\) satisfy the equation \[ dx_i(t) = -\mu _ix_i(t)dt+dA_i(t),\quad x_i(0) = x_i^0,\quad i=\overline {1,n}, \] \(\mu_i\) are some parameters, and \(A_i(t)\) are one-dimensional generalized Poisson processes with parameters \((\lambda _i,G_i(t))\). In this equation \(\{x_0,x_1,...,x_n\} \) is a sequence of observations of the process \(x(t)\). A method of parameter estimation for the unknown vector parameter \(\mu = (\mu _1,...,\mu _n)\) is proposed and consistency of the estimates is proved. Some modifications of the basic algorithm are proposed and the probability of exact estimation of the parameter \(\mu\) is obtained.
Reviewer: O.A.Voina (Kyïv)

MSC:

62P12 Applications of statistics to environmental and related topics
62M05 Markov processes: estimation; hidden Markov models
62F12 Asymptotic properties of parametric estimators
60J25 Continuous-time Markov processes on general state spaces
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