# Tagged Questions

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### Stability of simulation of brownian noise

As I understand, Brownian noise can be simulated by the process $$x_{n+1}=x_n+R_n$$ where $R\sim U[-a,a]$. The expected value for $x_n$ is then $x_0$. But $\text{Var} x_n\to\infty$ as $n\to\infty$ ...
I wrote a simulation of a geometric Brownian motion which works like this: $t_i - t_{ i-1 } \sim Exp(\lambda )$ $Z_i \sim N(0,1)$ $Y_i \sim e^{ \sigma \sqrt { t_i - t_{ i-1 } } Z_i +\left( \mu ... 0answers 29 views ### Simulation of a Bidimensional Fractional Brownian motion I would like to simulate and understand the simulation of a bidimensional fractional Brownian motion (I would like to try and use it to simulate terrain in a 3d game I am developing), but I cannot ... 0answers 43 views ### Simulating of GBM I have a question regarding the simulation of a GBM. I have found similar questions here but nothing which takes reference to my specific problem: Given a GBM of the form$dS(t) = \mu S(t) dt + ...
I am trying to simulate (for the first time) a 2-dimensional SDE, in Matlab. $$X(t)=F(t,X(t))\,dt + \sigma(t,X(t))\,dBt$$ I have no problem using the Euler-Maruyama method in the one dimensional ...