waves-16-arma

git clone https://git.igankevich.com/waves-16-arma.git
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commit 5d5b96bf3b9c7754242aeb1f15be1a8077317822
parent ac0a4ffbef95fd97ca086717d2d06bed4ee1a313
Author: Ivan Gankevich <igankevich@ya.ru>
Date:   Sun, 28 May 2017 20:03:50 +0300

Insert citations.

Diffstat:
arma.org | 17++++++++---------
refs.bib | 28++++++++++++++++++++++++++--
2 files changed, 34 insertions(+), 11 deletions(-)

diff --git a/arma.org b/arma.org @@ -182,12 +182,12 @@ Another approach to modelling wind waves is possible in terms of the representation of a stochastic moving surface as a linear transformation of white noise with memory. These methods are one of the most popular ways of modelling stationary ergodic Gaussian random processes with given correlation -characteristics (Box, et al., 2008). However, these methods have were not used +characteristics cite:box1976time. However, these methods have were not used to simulate wind waves for a long time. The first attempts to model -two-dimensional disturbances were undertaken in the early 70's (cf. Kostecki, -1972), and the impetus for this was the development of the resonance theory of -waves in wind. However, the formal mathematical framework was developed by -Gurgenidze & Trapeznikov (1988) and Rozhkov & Trapeznikov (1990). They built a +two-dimensional disturbances were undertaken in the early 70's (cf. +cite:kostecki1972stochastic), and the impetus for this was the development of +the resonance theory of waves in wind. However, the formal mathematical +framework was developed in cite:rozhkov1990,gurgenidze1988. They built a one-dimensional model of ocean waves \(\zeta(t)\), on the basis of an autoregressive-moving average (ARMA) model: \begin{equation} @@ -212,10 +212,9 @@ some substance in water etc.). Equation parameters are AR and MA process coefficients and order. Any ARMA process can be uniquely represented as a process moving average and -autoregression process of general infinite order (Gurgenidze & Trapeznikov, -1988), and the parameters of the spectral representation are defined by the rule -of division of power series (in a rational factorized form, Rozhkov & -Trapeznikov, 1990): +autoregression process of general infinite order cite:gurgenidze1988, and the +parameters of the spectral representation are defined by the rule of division of +power series (in a rational factorized form cite:rozhkov1990: \begin{equation*} S(\omega) = \frac{\Delta\sigma^2}{\pi} diff --git a/refs.bib b/refs.bib @@ -124,4 +124,29 @@ pages = {205--216}, year = {1983}, publisher = {Springer} -}- \ No newline at end of file +} + +@inbook{gurgenidze1988, + author = {Gurgenidze, A. T. and Y. A. Trapeznikov}, + title = {Probabilistic model of wind waves}, + booktitle = {Theoretical foundations and methods of calculating wind waves}, + address = {Leningrad}, + publisher = {Gidrometeoizdat}, + pages = {8--23}, + year = {1988} +} + +@book{rozhkov1990, + author = {Rozhkov, V. A. and Y. A. Trapeznikov}, + title = {Probabilistic models of oceanographic processes}, + address = {Leningrad}, + publisher = {Gidrometeoizdat}, + year = {1990} +} + +@phdthesis{kostecki1972stochastic, + title={Stochastic model of sea waves}, + author={Kostecki, M}, + year={1972}, + school={CTO, Gdansk} +}