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Michael Hardy
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Generating realizations from n$n$-dimensional geometric brownianBrownian motion where the variables are constrained to sum to 1

Is there a way to simulate an $N$-dimensional Geometricgeometric Brownian Motionmotion 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.

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.

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.

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Michael Hardy
  • 1
  • 12
  • 85
  • 126

Is there a way to simulate an N$N$-dimensional Geometric Brownian Motion i.e. variable $$x_i, i \ \epsilon \ [1, N] $$$$x_i, i \in [1, N] $$ is diffusing in log-space such that $$log\ (x_i)$$$$\log (x_i)$$ follows a Brownian motion with a given mean and variance and sum of all x_i$x_i$ is constrained to be 1.$1.$ 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.

Is there a way to simulate an N-dimensional Geometric Brownian Motion i.e. variable $$x_i, i \ \epsilon \ [1, N] $$ 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.

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.

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Is there a way to simulate an N-dimensional Geometric Brownian Motion i.e. variable $$x_i, i \ \epsilon \ [1, N] $$ 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.

Is there a way to simulate an N-dimensional Geometric Brownian Motion i.e. variable $$x_i, i \ \epsilon \ [1, N] $$ 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.

Is there a way to simulate an N-dimensional Geometric Brownian Motion i.e. variable $$x_i, i \ \epsilon \ [1, N] $$ 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.

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