Last data update: 2014.03.03
R: Generate a 2D Langevin process
timeseries2D R Documentation
Generate a 2D Langevin process
Description
timeseries2D
generates a two-dimensional Langevin process using a
simple Euler integration. The drift function is a cubic polynomial, the
diffusion function a quadratic.
Usage
timeseries2D(N, startpointx = 0, startpointy = 0, D1_1 = matrix(c(0, -1,
rep(0, 14)), nrow = 4), D1_2 = matrix(c(0, 0, 0, 0, -1, rep(0, 11)), nrow =
4), g_11 = matrix(c(1, 0, 0, 0, 0, 0, 0, 0, 0), nrow = 3),
g_12 = matrix(c(0, 0, 0, 0, 0, 0, 0, 0, 0), nrow = 3), g_21 = matrix(c(0,
0, 0, 0, 0, 0, 0, 0, 0), nrow = 3), g_22 = matrix(c(1, 0, 0, 0, 0, 0, 0, 0,
0), nrow = 3), sf = 1000, dt = 0)
Arguments
N
a scalar denoting the length of the time-series to generate.
startpointx
a scalar denoting the starting point of the time series x.
startpointy
a scalar denoting the starting point of the time series y.
D1_1
a 4x4 matrix denoting the coefficients of D1 for x.
D1_2
a 4x4 matrix denoting the coefficients of D1 for y.
g_11
a 3x3 matrix denoting the coefficients of g11 for x.
g_12
a 3x3 matrix denoting the coefficients of g12 for x.
g_21
a 3x3 matrix denoting the coefficients of g21 for y.
g_22
a 3x3 matrix denoting the coefficients of g22 for y.
sf
a scalar denoting the sampling frequency.
dt
a scalar denoting the maximal time step of integration. Default
dt=0
yields dt=1/sf
.
Details
The elements a_{ij} of the matrices are defined by the corresponding
equations for the drift and diffusion terms:
D^1_{1,2} = ∑_{i,j=1}^4 a_{ij} x_1^{(i-1)}x_2^{(j-1)}
with a_{ij} = 0 for i + j > 5 .
g_{11,12,21,22} = ∑_{i,j=1}^3 a_{ij} x_1^{(i-1)}x_2^{(j-1)}
with a_{ij} = 0 for i + j > 4
Value
timeseries2D
returns a time-series object with the generated
time-series as colums.
Author(s)
Philip Rinn
See Also
timeseries1D
Results