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2
votes
1answer
41 views
+50

Applying MCMC Metropolis algorithm

I'm interested in all possible paths (on the grid $\mathbb{N}^2 $) that goes from $ (0,0) $ to $ (n, n) $. At each step there are two possibilities: go right or go up. The path is a sequence $ ...
1
vote
1answer
21 views

Tissue Deformation Simulation using FEM

I need to simulate tissue deformation using FEM. Is it advisable to represent the object as a triangle mesh or a ...
0
votes
0answers
14 views

simulate inventory model with antithetic variable [closed]

I need make a simple program of the inventory model with scilab or matlab. I have the code but I need add the antithetic method for reduce the iterations's number with the variance reduction and I ...
0
votes
0answers
31 views

Understanding simulation of Brownian Motion

I am trying to understand the simulation of Brownian Motion given at http://www.math.uah.edu/stat/applets/BrownianMotion.html. There are four boxes in this simulation. For the purpose of this question ...
-1
votes
2answers
29 views

Calculating a Cardgame

I was send here from stackoverflow because they thought maybe you can help me. Here my original post: http://stackoverflow.com/questions/26799476/a-faster-way-then-doing-14-for-loops What I want: ...
0
votes
1answer
16 views

Incomplete Cholesky decomposition conjugate gradient method in Matlab

I have a problem in finding the numerical material that describing in detail for incomplete Cholesky combined with conjugate gradient method by using Matlab. Someone can help me? Many thank in ...
0
votes
0answers
9 views

Simulate and present normal distribution [migrated]

My task is to compare different methods of simulating normal distribution. For example, I use following code, to generate 2 vectors, each 1000 values (Box-Muller method): ...
0
votes
0answers
15 views

Skew in black scholes model

We are modeling Foreign exchange rates using Black Scholes model given below: $F_t = F_{t-1} + (r_d - r_f)F_{t-1} dt + \sigma\cdot F_{t-1}\cdot dW_t$ Where $F_t$ and $F_{t-1}$ are FX rates at time ...
0
votes
1answer
15 views

Angular momentum superposition

I am doing a space simulation. I have a spaceship and this spaceship has engines that don't push the spaceship through its center of gravity. These engines can therefore give the spaceship angular ...
2
votes
1answer
4k views

Can't understand a simple wave equation matlab code

I'm trying to figure out how to draw a wave equation progress in a 2D graph with Matlab. I found this piece of code which effectively draw a 2D wave placing a droplet in the middle of the graph (I ...
0
votes
0answers
14 views

Generate a random chain with cauchy distribution using C language

Here is my question: I want to simulate a random variable using cauchy distribution with C language. Scale and position must be setted manually. I fuond the GSL library wich contain the function: ...
0
votes
0answers
11 views

would the following game be beatable with martingale

I want to mix 2 games with weight on game one 51.5% and 48.5% on game two player will be presented with 3 coins and he will be asked to click on 1 of the 3 coins and then all 3 coins are turned ...
1
vote
1answer
329 views

Simulation of a Gaussian process on $R^2$ with a stationary kernel using the Karhunen-Loève expansion

Assume $X(\omega, t) \sim \mathcal{N}(0, K(\cdot, \cdot))$ is a real-valued, centered Gaussian process on $R^2$, i.e., $X: \Omega \times R^2 \to R$. Let the covariance function of the process be ...
0
votes
0answers
33 views

Uniform Sampling over Convex Polytope (not full-dimensional)

I want to simulate a uniform distribution on a convex polytope that is not full-dimensional for optimization purposes (to generate random points on the set I want to minimize over). The polytope is ...
3
votes
1answer
39 views

Hypercomputation & Higher Dimensional Variants of Conway's Game of Life

Conway's Game of Life is a simple and important mathematical game with some rules of evolution in a two dimensional space. It appears in many subjects in mathematics, artificial intelligence and ...
0
votes
0answers
14 views

R- generate sample that follows a geometric distribution

I'm having trouble coming up with an algorithm that generates a sample $(X_1,...,X_n)$ of size n, considering several values for n, where the random variable $X_i$ – “number of trials until the first ...
1
vote
0answers
19 views

Are these two approaches to calculating return rate mathematically consistent?

I have coded two C# programs, which use two different approaches to evaluate the outcome of a certain casino-style game (casino-style in the sense that the user pays points to take a turn, and ...
1
vote
0answers
50 views

Backward Euler method with a cross-product.

I want to solve the following differential equation with the backward Euler method ...
0
votes
0answers
18 views

Sampling from a random distribution with a margin of error

A survey of a population is taken using sampling. It is determined that 70% prefer option A and 30% prefer option B with a margin of error being 5%. Typically when simulating the process with the ...
0
votes
0answers
39 views

Transform this IVP into a first-order autonomous system with $\dot{x} = Ax + b$

I'm fairly new to differential equations and need some guidance with this following problem: Transform the following IVP into a first-order autonomous system in the form $\dot{x} = Ax + b$: $$ ...
0
votes
1answer
38 views

Conditional probability problem and Alias Method

I hopefully someone can help me with this problem of conditional probability: "A disk server receives requests from many client machines and requires 10 milliseconds to respond to each request. The ...
0
votes
0answers
29 views

Expected Probability of a Random Agent and a Probabilistic Agent

I'm running simulations on two agents: random agent and probabilistic agent. The world they are running in is the Wumpus World where the agent is dropped in a 4x4 grid where each cell has a 20% chance ...
2
votes
0answers
14 views

orderstatistics of uniform distributions on different ranges

During a simulation I discovered an interesting phenomenon: Given you have 3 agents. 2 are uniformly distributed between [0,1] and one between [0,2]. The question is how often do the smaller agents ...
0
votes
1answer
25 views

Simulating a controlled dynamical system

I am try to simulate a controlled dynamical system of the form $$\dot{x}=f(x,\phi(x)),$$ where $\phi$ is the controller. To do so, I am using Octave (an open source version of Matlab). My commands ...
0
votes
1answer
25 views

Approximation and Monte Carlo simulation.

I am a bit up over my head here, I will present an argument and then I hope you guys will say if my reasoning is correct or what should be changed, ultimately I am hoping to say something qualified ...
-1
votes
2answers
39 views

Wrong simulation

I am simulating $(1+\eta)^{19}$ where $\eta$ is exponentially distributed with mean 0.15. I'm suppose to get on average 21 thousands. But my code below never output anything above 100. What am I ...
0
votes
1answer
52 views

Simple Monte Carlo simulation/approximation of 2 pair in a 5 card poker hand

I am very curious about simulation of an event where an estimating/sampling technique is used. In this example, the goal is to simulate a subset of all the roughly $2.6$ million $5$ card poker hands ...
0
votes
0answers
13 views

Individual particle tracking simulation

I want to do a simulation of a stochastic system. I have 4 types of cell, each will divide or die with a certain probability. Let's say : A-> A+A A -> A+B A -> A+C B-> B+B B-> die and so on... ...
0
votes
1answer
29 views

Distribution of hitting position of line by brownian motion.

What is known about the distribution of the hitting position of a line by a 2d brownian motion? I've tried to make some simulations of a 2d brownian motion where every computational step has a ...
1
vote
0answers
77 views

Kalman Filter application to non-linear system.

I want to use the Kalman filter to have a better estimate of the state of a system which I know its equations of motion: ...
0
votes
2answers
28 views

How to calculate the direction (of velocity of a ball) after collision with another ball?

Say I have two balls of same radius, in the 2-D Plane. So like a pool (billiard) game. I have the cue ball, moving with the velocity vector V, the magnitude is not important, so we only need an angle ...
3
votes
0answers
40 views

Maximize or find an upper bound of the function $kx^{k-1}\exp(-\mu(x^k-x))$

I was programming some random variable simulation using the acceptance-rejection method and I encounter with the Weibull$(k,\lambda)$ distribution. This random variable is posible to simulate with ...
0
votes
0answers
64 views

Water swallowing in Matlab

I want to simulate some water passing through a vertical cylinder in Matlab, and I would like to implement a 3d animation of it. I built the cylinder using the patch function, but I do not know how to ...
0
votes
0answers
19 views

Simulation Lévy process

I need to simulate a Lévy process from its characteristic triple $(\gamma,\Sigma,\nu)$ where $\nu$ is the Lévy measure. I know that I can simulate it by summing a brownian motion and a compound ...
12
votes
3answers
373 views

Why can't you simulate isotropic fluid flow on a square lattice?

There are easy methods for discrete simulations of gas dispersion in two dimensions. If you take a large square lattice, each cell of which is assumed to contain at most one gas molecule, and you ...
0
votes
1answer
41 views

How to simulate from a simple point process

Define a point process by the conditional intensity function $$\lambda^*(t) = \mu + \alpha \sum_{t_i < t} e^{-(t-t_i)}$$ where $\mu$ and $\alpha$ are positive parameters. I would like to ...
6
votes
1answer
72 views

Distribution of time spent above $0$ by a Brownian Bridge.

Let's say I have a Brownian motion, such that I know its value at time 0 (0) and time T (also 0). I am trying to evaluate the time spent above 0 between time 0 and T. Obviously I know that the ...
1
vote
1answer
45 views

Simulate simple non-homogeneous Poisson proces

Consider a Poisson process whose conditional intensity is $$\lambda(t) = \alpha e^{-t}$$ starting at time $t=0$ for some parameter $\alpha>0$. I would like to simulate arrival/event/failure ...
0
votes
0answers
74 views

Estimation covariance of the Kalman filter state

I implemented Kalman filtering for a simplest 1D coordinate+velocity model. The prediction worked, but I wanted to estimate the prediction probability distribution. I.e. how likely it is that the ...
0
votes
0answers
10 views

Generating a given length sample and skewness whose normality is verified by one normality test but not by an other

I just want to generate 1 sample of length$=n>30$, |skewness$=S|<0.3$ and for which normality is not rejected by Shapiro wilk test of normality but rejected by Anderson darling test of ...
0
votes
0answers
13 views

spatial-partitioning based physical simulation

I've learnt that spatial-partitioning based physical simulation is kind of "approximate" computation. Is it because: since the whole space is partitioned into cells, and only the interactions of ...
1
vote
0answers
19 views

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 $n\to\infty$ ...
1
vote
1answer
57 views

Estimate arrival time of a ship given the average of the ships in a day in a Poisson Distribution

I'm working in a simulation of a Port where ships come to specific stations of the port. I already know that the average amount of ships is given by a Poisson distribution and the service time (On ...
1
vote
1answer
28 views

Simulation of orbiting bodies

I am writing a computer program to simulate orbiting bodies such as planets and stars. I wish to have a starting point in which a number of bodies are randomly scattered around a central heavy body. ...
1
vote
0answers
31 views

Distribution of phone calls during 24h

I would like to model the amount of phone calls at each time of the day. The phone calls should follow a poisson distribution and at 12:00 there should be the peak. So, semantically what I would like ...
11
votes
3answers
2k views

Simulating uniformly on $S^1=\{x \in \mathbb{R}^n \mid \|x\|_1=1\}$

A scheme to generate random variates distributed uniformly in $S^2=\{x\in \mathbb{R}^n \mid \|x\|_2=1\}$ is well known: generate a standard normal variate in $\mathbb{R}^n$ and normalize it to unit ...
0
votes
1answer
32 views

Simulation from cdf

Give a method for simulating from $$F(x) =\left\{\matrix{ \frac{(1-e^{-2x}+2x)}{3},& 0 < x < 1\cr \frac{3-e^{-2x}}{3}, & 1 < x < ∞}\right.$$ (Work out the pdf, and try to ...
-2
votes
2answers
58 views

Operations on distributions

Say we have two r.v X and Y which are independent and differently distributed ( for e.g X follows a bell curve and Y follows an exponential distribution with parameter $\lambda > 0$ What are the ...
0
votes
1answer
62 views

Continuum limit of cellular automata

Is there any function defined for say the plane, that has interesting nontrivial behaviour similar to Conway's Game Of Life, but where every point's on/off status is decided by something like the ...
0
votes
1answer
37 views

Calculate expectation under risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$

I am busy with a numerical simulation and I want the calculate the following expectation under the risk neutral measure: $\mathbb{E_Q}(\max(S-1,0))$. $S$ is some variable that I calculated using ...