Generate a 2D Langevin process
Description
timeseries2D
generates a twodimensional Langevin process using a
simple Euler integration. The drift function is a cubic polynomial, the
diffusion function a quadratic.
Usage
1 2 3 4 5 6  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 timeseries 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

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^{(i1)}x_2^{(j1)}
with a_{ij} = 0 for i + j > 5.
g_{11,12,21,22} = ∑_{i,j=1}^3 a_{ij} x_1^{(i1)}x_2^{(j1)}
with a_{ij} = 0 for i + j > 4
Value
timeseries2D
returns a timeseries object with the generated
timeseries as colums.
Author(s)
Philip Rinn
See Also
timeseries1D