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Filtering and parameter estimation in a simple linear system driven by a fractional Brownian motion
| Content Provider | Semantic Scholar |
|---|---|
| Author | Breton, Alain Le |
| Copyright Year | 1998 |
| Abstract | The problem of optimal ltering is investigated in a continuous time linear Gaussian system where the signal is a xed random variable and the noise driving the observation process is a fractional Brownian motion with Hurst parameter H 2 (1=2; 1). Closed form expressions are derived both for the optimal lter and the variance of the ltering error. Then an application to the determination of the best linear unbiased estimator in a related parameter estimation problem is discussed. Finally integral transformations which change a fractional Brownian motion to martingales are identiied and an elementary approach to a Girsanov type formula is developed which shows that the estimator is in fact the maximum likelihood estimator. |
| File Format | PDF HTM / HTML |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Brownian motion Deuterium Estimation theory Hurst exponent Linear system Normal Statistical Distribution Population Parameter Sample Variance cell transformation |
| Content Type | Text |
| Resource Type | Article |