stochint: Integrate one sample path of a stochastic process w.r.t....

In Uffe-H-Thygesen/SDEtools: Utilities for Stochastic Differential Equations

Integrate one sample path of a stochastic process w.r.t. another, returning the Ito integral, the Stratonovich integral, or the "right hand rule".

Description

Integrate one sample path of a stochastic process w.r.t. another, returning the Ito integral, the Stratonovich integral, or the "right hand rule".

Usage

stochint(f, g, rule = "l")

Arguments

f	numeric vector containing the integrator
g	numeric vector, same length as f, containing the integrand
rule	character vector indicating rule(s). Valid choices are "l", "r", or "c" for "left", "right", and "center", as well as combinations, e.g. c("l","c"). Optional and defaults to "l".

Value

A numeric vector, same length as f, giving the "running integral", i.e. the integral as a function of the upper limit.

Examples

## Integrating a cosine w.r.t. a sine
times <- seq(0,2*pi,length=21)
I <- stochint(cos(times),sin(times))
Ia <- 0.5*times+0.25*sin(2*times)  # Analytical result
matplot(times,I,type="l")
lines(times,Ia,col="blue",lwd=2)

## Integration of Brownian motion w.r.t. itself
times <- seq(0,10,0.01)
BM <- rBM(times)
I <- stochint(BM,BM,c("l","c","r"))
matplot(times,cbind(I$l,0.5*BM^2-0.5*times),type="l",xlab="Time",ylab="Left integral (Ito)",
         main="Integral of B.M. w.r.t itself")
matplot(times,cbind(I$r,0.5*BM^2+0.5*times),type="l",xlab="Time",ylab="Right integral",
         main="Integral of B.M. w.r.t itself")
matplot(times,cbind(I$c,0.5*BM^2),type="l",xlab="Time",ylab="Central integral (Stratonovich)",
         main="Integral of B.M. w.r.t itself")

Uffe-H-Thygesen/SDEtools documentation built on Jan. 15, 2025, 6:41 p.m.