On drift parameter estimation in models with fractional Brownian motion. (English) Zbl 1396.62190
Summary: We consider a stochastic differential equation involving standard and fractional Brownian motion with unknown drift parameter to be estimated. We investigate the standard maximum likelihood estimate of the drift parameter, two non-standard estimates and three estimates for the sequential estimation. Model strong consistency and some other properties are proved. The linear model and Ornstein-Uhlenbeck model are studied in detail. As an auxiliary result, an asymptotic behaviour of the fractional derivative of the fractional Brownian motion is established.
MSC:
| 62M05 | Markov processes: estimation; hidden Markov models |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 60J65 | Brownian motion |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
Keywords:
fractional Brownian motion; Brownian motion; parameter estimation; stochastic differential equation; sequential estimation; Ornstein-Uhlenbeck modelReferences:
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