11 votes

Antithetic method for monte carlo when bounds of the integral are infinite

The point to the method of antithetic variates is to improve on such direct sampling methods. What can make it work well is to re-express the integral as an expectation of something with respect to a ...
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9 votes
Accepted

Antithetic method for monte carlo when bounds of the integral are infinite

Your code does not correspond to your description of the problem, so it is not surprising that you are not getting the results you expected. The integral you want to approximate is $$ \int_0^\infty e^{...
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6 votes
Accepted

Sample uniformly from unit square conditioned on sum and product

Let's solve a generalization, so that we can obtain both solutions at once. Let $h:[0,1]^2\to\mathbb{R}$ be differentiable with derivative $\nabla h=(D_1h, D_2h).$ To avoid technical complications in ...
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3 votes

Markov Chain Monte Carlo with known normalisation

Another way of looking at the issue of approximating$$\mathfrak I = \sum_{x\in\mathfrak X} p(x)O(x)$$by stochastic techniques is to aim at adding primarily large values of $p(x)O(x)$. Assuming no ...
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1 vote
Accepted

How to simulate non-gaussian stochastic paths

Posting as an answer as too long for a comment: The reason you're seeing the central limit theorem crop up here is because your returns at each time point are independent. I think what you want to do ...
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