# Questions tagged [simulation]

A vast area which includes generating results from computer models.

205 questions
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### Proving that Markov Chain Monte Carlo converges

I am trying to understand how the very basic Markov Chain Monte Carlo approach works: We try to approximately calculate the expected value $E_{\pi(x)}[X]$ by drawing sequential samples from a Markov ...
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### How to simulate a Super-Brownian Motion (SBM)?

I'll start by doing this in MATLAB. A Standard Brownian Motion $dX_t$ can be approximated by a scaled random walk through $\triangle{X}=Z\sqrt{\triangle t}$. Analogously the drift of a Super-Brownian ...
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### How to implement an insurance risk model

So the problem goes as follows: "Suppose that the different policyholders of a casualty insurance company generate claims according to independent Poisson processes with a common rate $λ$, and that ...
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### Queuing system - advice needed on what models to use, and suitable free simulation software

There is a system consisting of: $\mathbf{Workcentres:}$ 6 workcentres $W_i$ assumed to be operating at different rates $\mu_{W_i}$, which depends on which input is being worked on. Assume there are ...
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### Simulate Brownian motion on a mesh surface

Does anybody know of any work on how to simulate Brownian motion on a mesh surface in $\mathbb{R}^3$ (i.e. treating it as an Ito process on a Riemannian manifold)? I'd like there to be a proof that ...
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### Studying the behavior of curious but timid animals

Let $\mathcal {G}$ be an $n\times n$ grid inhabited by $k$ animals, time is indexed by the naturals, the metric $d(x_i,x_j)$ on $\mathcal G$ between two animals $i$ and $j$ is the Manhattan distance. ...
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### Stochastic simulation Gillespie algorithm for areas instead of volumes?

I am trying to find resources on the Gillespie stochastic simulation algorithm for my system which happens on a surface. The original algorithm was developed for a reactor of volume $V$, but my system ...
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### “Change of measure” for fast simulation.

$\newcommand{\var}{\operatorname{var}}$The problem is here: Consider a nonnegative random variable X whose PDF is close to being exponential, of the form $$f_X(x) = g(x)e^{−x},$$ where $g(x)$ is a ...
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### Option pricing and mean reversion

In different books one can find a formula for option pricing when we assume that $\ln(S)$ follows a mean reversion process $$dS_t/S_t=\kappa(\theta-\ln(s)) - \ln(S)dt+\sigma dZ$$ If we calculate an ...
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### How to generate a large PSD matrix $A \in \mathbb{R}^{n \times n}$, where $\mathcal{O}(n) \sim 10^3$

I would like to generate a large PSD matrix, i.e., $A \in \mathbb{R}^{n \times n}$, where $\mathcal{O}(n) \sim 10^3$. The entries of the matrix should be randomly generated using a standard function ...
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### Simulation of fractional noncentral Wishart distribution

For a non-integer number of degrees of freedom $\nu > p-1$, one can simulate the central Wishart distribution $W_p(\nu, \Sigma)$ with the help of the Bartlett decomposition. How to simulate the ...
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### Simulation of Cox processes with self-dependent intensity

A Cox Process $X_t$ is, in a nutshell, a Poisson process whose intensity $\lambda_t$ is a stochastic process itself. If $\lambda_t$ is independent from $X_t$ and it's possible to sample, then one can ...
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### Metropolis-Hastings for doubly-unnormalised densities?

I wish to do inference in a joint space $P(x,y)$ that is particularly tricky, because I don't have access to an unnormalised density $f(x,y)\propto P(x,y)$. However, I do have: An unnormalised ...
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### Time oriented simulation

A factory y has large g number of semiautomatic machines.On 50% of the working days none of the machines fail. On 30%of the days one machines fails and on 20%of the days two machines fail. The ...