commit 5d5b96bf3b9c7754242aeb1f15be1a8077317822
parent ac0a4ffbef95fd97ca086717d2d06bed4ee1a313
Author: Ivan Gankevich <igankevich@ya.ru>
Date: Sun, 28 May 2017 20:03:50 +0300
Insert citations.
Diffstat:
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}
+}
