Abstract
Stationary and non-stationary processes. Practical difficulties characterising observed erratic time series. Characterising time series using the structure function, autocorrelation, and the periodogram. Moving Average processes. Autoregressive processes. Poisson processes and shot noise. Conceptual differences in continuous random processes. Stochastic differential equations and how to solve them. The Ornstein–Uhlenbeck process and related processes. Markov chains.
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Notes
- 1.
At a detailed level, different authors define the periodogram in subtly different ways—careful reading required!
- 2.
There are some subtly different conventions for normalising Wiener noise in the literature, so do read carefully.
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Lawrence, A. (2019). Erratic Time Series. In: Probability in Physics. Undergraduate Lecture Notes in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-04544-9_12
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DOI: https://doi.org/10.1007/978-3-030-04544-9_12
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