Questions tagged [simulation]

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What new fractional brownian motion (fBm) simulation methods have emerged since 2010? [closed]

I want to describe new methods for simulating fBm, as in the work of Coerjolly and Dieker, but new methods are not very easy to find.
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1 vote
0 answers
46 views

Real life applications of distributions through models or simulations [closed]

What are the areas we can apply distributions in classical harmonic analysis? I don't mean probability distributions but distributions that are continuous linear functionals on the space of test ...
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6 votes
1 answer
403 views

Is this a Brownian motion?

I am building a 2D stochastic process as follows. I start with a point $P_0=(0,0)$. Then $P_k=(X_k,Y_k)$ is defined as follows, for $k>0$: \begin{align} X_k & =X_{k-1}+R_k \cos(2\pi\theta_k) \\ ...
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4 votes
0 answers
181 views

From biased coins to biased coins, as efficiently as possible

Background We're given a coin that shows heads with an unknown probability, $\lambda$. The goal is to use that coin (and possibly also a fair coin) to build a "new" coin that shows heads ...
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6 votes
0 answers
268 views

Concave functions: Series representation and converging polynomials

Background We're given a coin that shows heads with an unknown probability, $\lambda$. The goal is to use that coin (and possibly also a fair coin) to build a "new" coin that shows heads ...
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10 votes
0 answers
521 views

From biased coins (and nothing else) to biased coins

Background We're given a coin that shows heads with an unknown probability, $\lambda$. The goal is to use that coin (and possibly also a fair coin) to build a "new" coin that shows heads ...
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  • 503
0 votes
1 answer
87 views

Sampling uniformly in a ball of radius $\epsilon$ in the space of dicrete r.v. of m modalities for the total variation metric

I am looking for some reference or an algorithm that allows to sample uniformly in the ball centered at a discrete random variable of n modalities in the TV distance. For the record for 2 discrete ...
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0 votes
1 answer
60 views

Simulation of multivariate logistic distribution conditional to a plane

For an algorithm, I have to simulate $X_1, \ldots, X_n \sim_{\text{iid}} \text{Logistic}(0,1)$ conditionally to the event $(X_1, \ldots, X_n) \in P$, where $P$ is an affine plane in $\mathbb{R}^n$. I ...
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1 vote
2 answers
101 views

Another question on provable non-existence of an efficient deterministic numerical method

Herewith I submit what may or may not be considered a simpler version of this question. The question is whether it is provable that there is no efficient deterministic numerical method for a ...
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4 votes
1 answer
147 views

Intractability of an integral by deterministic numerical methods

Suppose $X_1,\ldots,X_n$ is an i.i.d. sample from a probability distribution with continuous c.d.f. $F.$ Let $F_n$ be the empirical c.d.f. $$ F_n(x) = \frac 1 n \sum_{k=1}^n \mathbf 1_{X_n\le x} = \...
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2 votes
1 answer
100 views

How far away is $\max_{x: x \in \{0, \ldots, N\}} |W(x/N)|$ from $\max_{0 \leq t \leq 1} |W(t)|$ ($W(t)$ a Wiener process)?

How far away is $$\max_{x: x \in \{0, \ldots, N\}} \left|W\left(\frac{x}{N}\right)\right|$$ from $$\max_{0 \leq t \leq 1} |W(t)|$$ In other words, if you simulate a Wiener process over a finite ...
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2 votes
0 answers
400 views

Convergence Based on Recurrence Relation

I am studying a sequence based on the following recurrence: $$X[t] = \sqrt{\alpha X[t-1]^2+(X[t-1]^2-\alpha X[t-2]^2)\frac{(2-X[t-1])^2}{X[t-1]^2}}$$ $$X[0]=0$$ $$X[1]>0$$ $$\alpha \in (0,1)$$ I ...
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2 votes
1 answer
315 views

Multiple Wiener-Ito integral distribution

Distribution of standard Ito integral is well known: $$I_1(f) = \int_0^T f(t)dB(t) \sim \mathcal{N}\bigg(0, \int_0^T f^2(t)dt\bigg).$$ Is it possible to find the distribution of multiple Wiener-Ito ...
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2 votes
1 answer
991 views

Design a Galton Board to simulate a uniform distribution

This link http://mathworld.wolfram.com/GaltonBoard.html suggests that a certain specific placement of pegs can be used to simulate a binomial or a normal distribution. Is there a specific peg ...
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4 votes
1 answer
104 views

How to simulate the fractional noncentral Wishart distribution?

I already asked this question on math.stackexchange but got no answer. For a non-integer number of degrees of freedom $\nu > p-1$, one can simulate the central Wishart distribution $W_p(\nu, \...
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4 votes
1 answer
429 views

How to draw a random normal matrix?

I would like to pick a random real normal (i.e. commuting with its transpose) matrix and I wonder if it can be done easily. I thought whether it would be possible to use a similar trick to drawing a ...
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2 votes
0 answers
51 views

brownian motion of 100 nm spherical particles in evenly spaced arrays [closed]

Generally looking for perspective from the computational experts. Question comes down to how tractable is the following problem. Let's say at time 0, I have a 2-D array of $N = 10$ spherical particles ...
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3 votes
1 answer
774 views

Sampling from a particular multivariate probability distribution

Given $3$ real variables $x_1, x_2, x_3 \equiv \bf{x}$, consider their probability density function (PDF) \begin{equation} P({\bf x}) = C \, p(x_1) \cdots p(x_3) \exp[f({\bf x})], \end{equation} where ...
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5 votes
2 answers
1k views

Real world example of use of Monte Carlo method for high dimensional integrals

The Monte Carlo method for numerical integration is usually presented as a method invented to efficiently compute high dimensional integrals numerically. However, I haven't found any source which has ...
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1 vote
0 answers
157 views

A mathematical biology reference request

Is there any mathematical articles that describe the differential equation modelling of locomotion of amoeba using pseduopodia? I am looking for physics based models of pressure difference modeling of ...
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4 votes
0 answers
103 views

Designing Character Other Than Temperature for Simulated Annealing on Combinatorial Optimization

Many research on designing temperature for simulated annealing is carried out. We wonder if there is any research on designing general feature of the Hamiltonian used in Simulated Annealing. For ...
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1 vote
1 answer
86 views

Choose uniformly from fixed-length paths in $[0,n]\cap\mathbb{Z}$ with fixed start and end

Let $X_k$ be a symmetric (discrete time) random walk on $\mathbb{Z}$ and let $m,n\in\mathbb{N}$. I want to chose uniformly from the paths of $X_k$, which start at $0$ stay in $[0,n]\cap\mathbb{Z}$ ...
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1 vote
0 answers
110 views

Monte Carlo Simulation - efficient simulation of tail outcomes [closed]

When running Monte Carlo type simulations in situations where you're only interested in tail outcomes, do you know of a way to only simulate those outcomes, so that you can come up with more reliable ...
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1 vote
0 answers
77 views

Importance sampling for bernoulli-sequence, favouring long sequences of ones

Assume we have a sequence of i.i.d. bernoulli-distributed random variables of length $n$. I'm interested in doing rare event simulation and my event depends, among other random factors, on the ...
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1 vote
0 answers
482 views

9-point stencil "equivalent" for advection equation [closed]

So I inherited from some people a code that solves the advection-diffusion-reaction equation for a particular system. The original code was first implemented in 1D which worked fine in cartesian ...
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2 votes
0 answers
82 views

Customers and Anti-Customer Queueing Problem: What is the Customer delete probability

Hello may I ask for your help? First the setting: I have got a problem with some queueing theory. The whole problem would be a grid of nodes, all nodes have an operation intensity $\mu_{i,j}$. ...
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  • 21
0 votes
1 answer
522 views

Generating random variables from the Cantor Distribution [closed]

I am looking for a method (exact, if possible, but at least asymptotically correct) for generating random variates from a Cantor Distribution? It seems like its abstract definition prevents this. In ...
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0 votes
0 answers
80 views

how to efficiently compute the mean function for non-homogeneous poisson process?

Suppose that I know all intensity functions lambda(t) during given period [0,t], how can I compute the mean function m(t) for non-homogeneous Poisson process? Basically, m(t) in the integral of ...
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1 vote
1 answer
255 views

Condition Number and CFL Condition in Finite difference Methods [closed]

when applying a Finite Difference scheme for an IVP, two factors come to mind when considering stability: One factor would be the condition number of the approximation operator. The other factor ...
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3 votes
1 answer
79 views

Finite differencing scheme for Hamilton's equation with planar linkages

I am trying to simulate the movement of a planar linkage in the plane whose position and momentum obey Hamilton's equations, which is to say that $${{dq}\over{dt}} = {{dH}\over{dp}}$$ and $${{dp}\...
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0 votes
0 answers
382 views

Monte carlo Method to estimate a proportion

I'd like to use Monte Carlo method to estimate a proportion and I'd like to be sure my idea is correct mathematically speaking. Let a pool full of red and blue balls. I'd like to estimate the ...
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11 votes
3 answers
2k views

On mathematical studies of the Mpemba effect

Since the days of Aristotle and Descartes, it has been known that under certain circumstances warm water freezes faster than cold water. This effect is now commonly known as the Mpemba effect, named ...
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2 votes
2 answers
155 views

Drawing random variates from a partially described probability distribution

I have a probability distribution over $\{0,1\}^n$ but instead of knowing the full joint distribution $p(x_1,\dots,x_n)$, I only know $p(x_i=x_j)$ for each $i,j$. How could I draw a random binary ...
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8 votes
1 answer
1k views

What is the "Tangle" at the Heart of Quantum Simulation?

The following questions generalize and naturalize the question that was originally asked. Provisional answers largely due to Will Sawin are now included. As was discussed in the question originally ...
2 votes
0 answers
149 views

A question on discrete numerical simulation on fluids mechanics

I read the paper "Stable, circulation-preseving simplicial fuids" by Elcott, et al: http://www.cs.jhu.edu/~misha/Fall09/Elcott07.pdf. It gives a structure preseving discretization of fluids. I have ...
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1 vote
1 answer
143 views

Staggered timing on 2-D random walks by multiple agents

In 2-D lattice random walks by multiple drunks who can't step onto each other, mathematically I would just say the whole cellular automaton updates "at once". But to simulate this on a computer, I ...
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3 votes
0 answers
631 views

Monte Carlo sampling high dimensions with the halton sequence?

Referring to the Halton Sequence, Swiler et al 2006 state that In cases where a large number of input variables are sampled, Robinson and Atcitty recommend using a leaped sequence, where the ...
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0 votes
0 answers
463 views

Simulating conditional expectations

There is a multidimensional process X defined via its SDE (we can assume that its a diffusion type process), and lets define another process by $g_t = E[G(X_T)|X_t]$ for $t\leq T$. I would like to ...
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0 votes
1 answer
193 views

How are epidemic models simulated in case of mobility?

I am not a mathematician but out of curiosity I am trying to implement the SIS epidemic model when the nodes have mobility to understand how it will change the results. I understand how to perform ...
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3 votes
2 answers
672 views

Is it possible to reliably generate a particular approximation of an ideal knot via a simulated annealing approach?

Say I take a cord, tie a loose knot in three-dimensional space, and pull tightly on the ends to generate an approximation of an ideal knot. If the cord has a fixed knot topology and a random initial ...
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10 votes
1 answer
818 views

exactly simulating a random walk from infinity

In diffusion-limited aggregation on the square lattice, one lets a particle do "random walk from infinity" until it hits the current aggregate, at which point the site occupied by the particle is ...
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1 vote
4 answers
3k views

Will a random walk on [0, inf) tend to infinity? [closed]

Consider a random walk on [0, inf) where you start at 0. With probability p = 0.5, you increase by 1. With probability (1-p) = 0.5, you decrease by 1, but not below 0. As time goes to infinity, will ...
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6 votes
1 answer
3k views

How can I generate the simulated time series

I am curious how one can generate simulated time series data. I found a list of simulated series here and a similar tool for stock market. What is the best way to generate domain specific time series ...
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8 votes
1 answer
423 views

Potts model simulation

I was wondering what were the state-of-the-art methods to simulate low temperature configurations of Potts-like models that exhibit a discontinuous phase transition. For models with a continuous phase ...
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1 vote
1 answer
342 views

[Numerical Mathemtics] How to solve hexagonal central differences

I want to simulate a 2d linear wave equation on a circle ($\displaystyle\frac{\partial^2 z(x,y,t)}{\partial t^2}=v^2\cdot\left(\displaystyle\frac{\partial^2 z(x,y,t)}{\partial x^2}+\displaystyle\frac{\...
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1 vote
1 answer
1k views

Monte Carlo sampling from correlated empirical distributions

I have a dataset that contains six correlated variables, and I want to sample new data so that each variable has the same marginal distribution as the original data, and the correlations are also the ...
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6 votes
2 answers
393 views

how to sample a conditioned diffusion

there are several reasons why we could be interested in sampling conditioned diffusions: if we observed a diffusion at discrete time and want to do some kind of inference on the parameters of the ...
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