Langevin (version 1.3.3)

timeseries1D: Generate a 1D Langevin process

Description

timeseries1D generates a one-dimensional Langevin process using a simple Euler integration. The drift function is a cubic polynomial, the diffusion function a quadratic.

Usage

timeseries1D(
  N,
  startpoint = 0,
  d13 = 0,
  d12 = 0,
  d11 = -1,
  d10 = 0,
  d22 = 0,
  d21 = 0,
  d20 = 1,
  sf = 1000,
  dt = 0
)

Value

timeseries1D returns a time-series object of length N with the generated time-series.

Arguments

N

a scalar denoting the length of the time-series to generate.

startpoint

a scalar denoting the starting point of the time series.

d13, d12, d11, d10

scalars denoting the coefficients for the drift polynomial.

d22, d21, d20

scalars denoting the coefficients for the diffusion polynomial.

sf

a scalar denoting the sampling frequency.

dt

a scalar denoting the maximal time step of integration. Default dt=0 yields dt=1/sf.

Author

Philip Rinn

See Also

timeseries2D

Examples

# Generate standardized Ornstein-Uhlenbeck-Process (d11=-1, d20=1)
# with integration time step 0.01 and sampling frequency 1
s <- timeseries1D(N=1e4, sf=1, dt=0.01);
t <- 1:1e4;
plot(t, s, t="l", main=paste("mean:", mean(s), " var:", var(s)));