Skip to main content
4 of 5
deleted 3 characters in body
Michael Hardy
  • 1
  • 12
  • 85
  • 126

Generating realizations from n-dimensional geometric brownian motion where the variables are constrained to sum to 1

Is there a way to simulate an $N$-dimensional Geometric Brownian Motion i.e. variable $$x_i, i \in [1, N] $$ is diffusing in log-space such that $$\log (x_i)$$ follows a Brownian motion with a given mean and variance and sum of all $x_i$ is constrained to be $1.$ I don't know much about this topic so any references would be really useful.

Additionally can mean and variance of each variable be selected independently of each other.