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I have to simulate a homogeneous Poisson Point Process on $\mathbb{R}^2$ with fixed number of points. Any hints as to how to do it would be helpful. I know that for a bounded region W we first generate a random variable M with a Poisson distribution with mean βA(W), where A(W) is the area of W. Given M = n, we then generate n independent uniform random points in W. But how do we do it when W is whole of the $\mathbb{R}^2$ plane

user254545
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    Because the event of getting a finite number of points on $R^2$ is of zero probability and can't be reasonably approximated, I see no way to generate these points. You basically needs to generate each point uniformly in $R^2$ which is not possible. The conditional distribution you are trying to generate from is not well-defined. – A.S. Mar 08 '16 at 06:43
  • I was thinking along the same lines, but I wasn't sure. The second step to it is that the points of the process are in Brownian motion in $\mathbb{R}^2$, so can I just simulate these points in a bounded region and then give them whole of $\mathbb{R}^2$ to move on. But I don't know how to achieve this. – user254545 Mar 08 '16 at 06:52
  • If your problems is ill-defined, any result is good. So put all $n$ starting points at the origin and let them run. As good as any other choice in this case. – A.S. Mar 08 '16 at 06:54

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