Discretely Observed Brownian Motion Governed by Telegraph Process: Estimation
| Autor: | L. Mark Elbroch, Thomas H Meyer, Jun Yan, Vladimir Pozdnyakov, Anthony Labarga |
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| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Mathematical optimization Markov chain Stochastic process General Mathematics 010102 general mathematics Markov process Markov model 01 natural sciences Time reversibility 010104 statistics & probability symbols.namesake Markov renewal process symbols Markov property Statistical physics 0101 mathematics Telegraph process Mathematics |
| Zdroj: | Methodology and Computing in Applied Probability. 21:907-920 |
| ISSN: | 1573-7713 1387-5841 |
| DOI: | 10.1007/s11009-017-9547-6 |
| Popis: | A Brownian motion whose infinitesimal variance alternates according to a telegraph process is considered. This stochastic process can be employed to model a variety of real-word situations, such as animal movement in ecology and stochastic volatility in mathematical finance. The main goal is to develop an estimation procedure for the underlying model parameters when the process is observed at discrete, possibly irregularly spaced time points. The sequence of observations is not Markov, but the sequence of the state of the telegraph process, if observed, is Markov. The observed sequence is therefore from a hidden Markov model. Likelihood inference is developed via dynamic programming, and is demonstrated to have much higher efficiency than the composite likelihood approach that was applied in an earlier work. The model is applied to model the movement of a mountain lion. |
| Databáze: | OpenAIRE |
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