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On estimation of the linearized drift for nonlinear stochastic differential equations. (English) Zbl 1064.62092

Summary: The estimation of the linearized drift for stochastic differential equations with equilibrium points is considered. It is proved that the linearized drift matrix can be estimated efficiently if the initial condition for the system is chosen close enough to the equilibrium point. Some bounds for initial conditions ensuring the asymptotical efficiency of the estimator are found.

MSC:

62M05 Markov processes: estimation; hidden Markov models
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93E15 Stochastic stability in control theory
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[1] DOI: 10.1090/pspum/057/1335496 · doi:10.1090/pspum/057/1335496
[2] DOI: 10.1007/BFb0076837 · doi:10.1007/BFb0076837
[3] DOI: 10.1016/S0304-4149(97)00083-5 · Zbl 0933.62099 · doi:10.1016/S0304-4149(97)00083-5
[4] DOI: 10.1007/s004400050213 · Zbl 0980.62090 · doi:10.1007/s004400050213
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