OUanalytic: Ornstein-Uhlenbeck analytic expression

In williamjsdavis/ItoGaussPlot: Calculate Ito-Gauss plot

Ornstein-Uhlenbeck analytic expression

Description

\loadmathjax

The closed form expression of slope standard deviation, for an Ornstein-Uhlenbeck process.

\mjeqn\sigma

_B(w) = \sqrt24\gamma D f(\gamma w),

where \gamma is the slope of the drift term, D is the amplitude of the noise term, and f(w) is

\mjeqn

f(x) = x^-3-3x^-4+12x^-6-e^-x\Big(3x^-4+12x^-5+12x^-6\Big).

Usage

OUanalytic(windowLength, gamma, D, approx="none")

Arguments

windowLength	Length of window, scalar or vector, float
gamma	Slope of drift term, scalar, float
D	Amplitude of noise term, scalar, float
approx	Approximation type (optional, defaults to "none"), string: none/smallW

Details

If 'windowLength' is a vector, the function will broadcast over it.

Examples

## Broadcasting over a vector of windows
> OUanalytic(10^seq(-1,2,len=5), 1, 1, "none")
[1] 4.798460391 1.843358930 0.495709635 0.059640405 0.004824965

williamjsdavis/ItoGaussPlot documentation built on Oct. 18, 2023, 4:20 p.m.