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2
votes
2answers
42 views

Analytic methods vs Monte Carlo (terminology)

What's the correct terminology to say "We can calculate the probability exactly using pure math, as opposed to Monte Carlo simulation"? Analytically sounds like we need Calculus, which we may not ...
1
vote
1answer
23 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
1answer
64 views

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 ...
1
vote
1answer
53 views

Calculating cumulative Markov Chain outcomes

I have a Markov process, with 2 possible states (1 or 0) and a transition matrix P. State at time t=n is determined by x0*Pn. As n goes to infinity, xn goes to the steady state vector, q = [q1 q2]. ...
1
vote
1answer
34 views

Simulation of typical cell in Poisson Voronoi tessellation

I would like to simulate a typical cell in Poisson-Voronoi tessellation model. I want to save the Cartesian coordinates of all vertices of the typical cell for each realization. How to do it? Thank ...
1
vote
1answer
45 views

Is it allowed to use the quadratic solution formula for a differential equation

I have some trouble with a challenging fluid mechanics problem. The problem leads me to a non-linear ode 1st order. $0={\dot p_C}^2+\frac{k_1}{k_2 C}\dot p_C+\frac{p_C-p_0}{k_2C^2}$ My Idea was now ...
0
votes
1answer
27 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 ...
0
votes
1answer
28 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 ...
0
votes
1answer
17 views

Determining simulation threshold

Let's suppose we have some sort of game (for instance tic-tac-toe) with a limited amount of moves. I want to simulate that game, and with that I will use a random number generator (RNG) to calculate ...
0
votes
1answer
31 views

Finding variance .

Suppose that $f : [0, 1] → [0, 1]$ and we wish to estimate $$I = \int_{0}^{1} f(x) dx$$ Using the hit-and-miss method, we obtain the estimate $$\hat I_{HM}=\frac{1}{n}\sum_{i=1}^{n}X_i$$ where ...
0
votes
1answer
52 views

How to resolve this?

I've the following problem to model and program it: suppose that we have a central server that provides 3 different services($S_1,S_2,S_3$), there are $N$ machines connected to this server: each ...
0
votes
1answer
53 views

Comparing speed in stochastic processes generated from simulation?

I have an agent-based simulation that generates a time series in its output for my different treatments. I am measuring performance through time, and at each time tick the performance is the mean of ...
0
votes
1answer
61 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 ...
-1
votes
1answer
111 views

How does the NCT model take angular velocity into account? (Nearly coordinated turn)

In a Kalman filter taking into account NCT, the state matrix is [x; vx; y; vy; omega]. Where omega is the angular velocity. What I don't understand is that when the F matrix for NCT is F=[ blah ...
4
votes
0answers
21 views

time spent by the brownian bridge above 0

Let's say I have a Brownian motion, such that I know it's value in 0 (0) and it's value at time T (also 0). I am trying to evaluate the time spent above 0 between time 0 and T. Obviously I know that ...
3
votes
0answers
64 views

Classify knots in a closed bead-spring like polymer simulation

my problem is to detect the crossing number (or another knot invariant) of a simulated polymer. A polymer is a closed bead spring, which mean that it is represented by a set of points connected by ...
3
votes
0answers
177 views

Simulation and Stochastic Processes

Supposing we want to take a sample from the distribution $p(x)=cp^*(x)$ where $c$ is the normalization constant and $p^*(x)$ is given by $$p^*(x)=0.5\exp(-(x-\mu_1)^2)+0.5\exp(-(x-\mu_2)^2).$$ ...
2
votes
0answers
105 views

Positive eigenvalues in differential-algebraic equations not appearing in time-domain simulation

I am solving a system of equations derived from power system applications. It consists of index-1 differential and algebraic equations in the form: $$\dot{x}=f(x,y) \\ 0=g(x,y)$$ To get the ...
2
votes
0answers
119 views

Simulating first passage times

I have a Brownian motion $X_t = \mu t+\sigma W_t$, where $W_t$ standard Brownian motion. I know that the first passage time $\tau = \min\{t|X_t\leq\alpha\}$, is Inverse Gaussian distributed i.e., ...
1
vote
0answers
18 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
0answers
28 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 ...
1
vote
0answers
25 views

Forest fire simulation; analytically constructing a function for tree residual after fire

Consider a Cellular Automaton with an $n \times n$ grid, where each cell corresponds either to a tree or dirt. We assign a tree to cell $(i,j)$ by probability $p$. Next, we initiate a fire in some ...
1
vote
0answers
53 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: ...
1
vote
0answers
24 views

simulate hitting time of Brownian motion

let's say I have a brownian motion $W_t$, and I know the value of $W_1$. Is there a way to simulate the hitting time of $W_t$ and a given function $f(t)$ ? For instance I know that if $f(t)$ is a ...
1
vote
0answers
37 views

Random graphs simulation

Reading the article "Emergence of scaling in random network, by Barabasi and Albert" I faced a lot of results obtained by simulations of the A-B random graph model. I always wanted to do such ...
1
vote
0answers
50 views

Samples from the Dirichlet measure

In Ferguson, 1973, Definition 2, he defines a sample of size $n$ from a random probability measure $G$ on $(\mathcal{X}, \mathcal{B})$ as: $$ P(X_1 \in C_1, \cdots, X_n \in C_n | G(A_1), \cdots, ...
1
vote
0answers
29 views

Single evaluation for using exponential sampling until past a point

I am trying to improve an algorithm that looks like the following (and am getting stumped): I am provided with a starting time, rate, and a target time. I then use an exponential distribution to ...
1
vote
0answers
43 views

Simulating of GBM

I have a question regarding the simulation of a GBM. I have found similar questions here but nothing which takes reference to my specific problem: Given a GBM of the form $dS(t) = \mu S(t) dt + ...
1
vote
0answers
97 views

Approximation of SDE

I have been struggling with the following problem: If you want to find a numerical result by simulating the paths of a stochastic differential equation, in particular a geometric brownian motion I ...
1
vote
0answers
102 views

Maximizing noisy unknown function

I'm interested in maximizing a function $f(\mathbf \theta)$, where $\theta \in \mathbb R^p$. The problem is that I don't know the analytic form of the function, or of its derivatives. The only thing ...
1
vote
0answers
164 views

Expected value involving a conditional multinomial distribution

$X|z$ has a multinomial distribution $MN(m, \mathbf{q}(z))$ where $z$ is either 0 or 1 with probability $1/2$. I need to find: $E_X[\max\{\Pr(z=1|X), \Pr(z=0|X\}]$. Is there an analytical form to ...
1
vote
0answers
235 views

Semi implicit integration - stability issues

I am trying to decide whether to use semi-implicit integration vs. explicit integration (particularly Position Verlet over Semi implicit Euler). Although the Verlet approach is widely used and is ...
1
vote
0answers
162 views

Optimization via Simulation

I want to minimize and objective function $\hat{B_i}$ $i\in l$, which can be computed by a matlab code (assume $\operatorname{findB}(a, b, c)$ returns $B$. I have the following optimization problem: ...
1
vote
0answers
161 views

Markov Chains - Using Gibbs & Metropolis algorithm.

Suppose $f_x,_y$ is bivariate normal distribution. I was given the parameters $(μ_1, μ_2, σ_1^2, σ_2^2)$ and $ρ=0.95$ the correlation coefficient. I want to generate $(x_1,y_1), ...
0
votes
0answers
8 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
8 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
12 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 ...
0
votes
0answers
34 views

Let X be exponentially distributed with mean 1. Let Y|X=x be exponential with mean x. You are interesting in estimating P($XY\leq3$).

I have some difficulties with homework. And I would be glad if you help me. Let X be exponentially distributed with mean 1. Let Y|X=x be exponential with mean x. You are interesting in estimating ...
0
votes
0answers
11 views

Is there a 'mild' product function?

I'm simulating an economy, each person has a list of integers representing the quantity of each resource they possess (for example: 5 water, 6 food, 2 education). From this I want to calculate ...
0
votes
0answers
113 views

How to count discarded entities in a FIFO queue using Simulink?

I'm trying to model a single queue, single server simulation using Simulink in MATLAB, I've recently installed it and I'm pretty new. I've created a Time-Based Entity Generator (with an exponential ...
0
votes
0answers
14 views

interpolation linear for a sample path

I am looking for a couple of references: interpolation linear for a sample path of Brownian Motion
0
votes
0answers
36 views

Are my estimates of parameters of geometric brownian motion correct?

I wrote a simulation of a geometric Brownian motion which works like this: $t_i - t_{ i-1 } \sim Exp(\lambda )$ $Z_i \sim N(0,1)$ $Y_i \sim e^{ \sigma \sqrt { t_i - t_{ i-1 } } Z_i +\left( \mu ...
0
votes
0answers
16 views

Coverage of squares by randomly putting circles with width following a Gaussian distribution

For some reason, I need to know the coverage of squares, if I put circles randomly on them. The radius of my circles follow a Gaussian distribution. For a better understanding see the attached ...
0
votes
0answers
51 views

Transition probability for time-homogeneous and inhomogeneous models

Consider the below matrices with four states - $0 , 1 , 2 , 3$ to be modelled by the means of a time-inhomogeneous discrete-time Markov chain. It's assumed the transition probabilities remain constant ...
0
votes
0answers
29 views

Simulation of a Bidimensional Fractional Brownian motion

I would like to simulate and understand the simulation of a bidimensional fractional Brownian motion (I would like to try and use it to simulate terrain in a 3d game I am developing), but I cannot ...
0
votes
0answers
17 views

Monte Carlo by point or by interval

Say I compute monte carlo output from input scenarios. Input are discrete time series. I choose time series as an example to make the problem more obvious - this could be also any curve. Computation ...
0
votes
0answers
29 views

Determine whether intersecting sphere moves towards cuboid?

I am programming a physics simulation in which I check every frame of a sphere intersects a cuboid. If it intersects, I want to check if the sphere moves "towards" the cuboid in a sense. If it does, ...
0
votes
0answers
22 views

Discrete models of 2 dimensional wave propagation

Usually most 2-d dimensional propagator waves are modeled by some general equation such as d/dt^2 = laplacian; However, if discretized, this sometimes only gives off (x,y) -> (x+1,y), (x-1,y), ...
0
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0answers
23 views

Comparing two simulation models

I have been working on two simulation models where I try to estimate rare probabilites in discrete-time Markov chains. The first method I use is Importance Sampling where I use an approximation of ...
0
votes
0answers
32 views

STINT Approximate stochastic integrals

This is a matlab code to simulate stochastic integrals: ...