Questions tagged [random-process]
The random-process tag has no usage guidance.
50
questions
10
votes
1answer
248 views
Generating random sequence of integers with ordering constraints
I would like to write a Mathematica routine for generating random musical melodies that obey (some of) the constraints of traditional tonal harmony. For simplicity's sake, I'm interested only in ...
7
votes
1answer
803 views
How can I generate the same random number in Mathematica and MATLAB?
As a part of my research studies, I have developed a code which is essentially based on random generation of numbers. The first version of the code was written in MATLAB, however, for some reasons I ...
1
vote
1answer
30 views
Generate a normalized Haar-random vector
What is the procedure to generate a random qutrit quantum state?
That is, I want to generate a $3 \times 1$ vector $u$ such that $u$ is generated by a Haar random $3 \times 3$ unitary $U$ multiplied ...
1
vote
1answer
68 views
Correlated random field generation
I need to generate two correlated gaussian random fields. As far as I know, this question and this other provides the means to generate a single autocorrelated process. However, I am clueless about ...
1
vote
0answers
56 views
Stochastic noise with known propability density function
How can I generate samples for random function, which functional "probability density" is known? When I say "probability density" for random function $\xi(\mathbf{q},t)$, I mean, ...
2
votes
1answer
69 views
Existing template for coalescing random walk
I would like to simulate a 2-dimensional random walk on a lattice where the particles coalesce/merge when they occupy a similar site on the lattice. Would it be possible to tweak in an efficient way ...
6
votes
1answer
260 views
Animating a random walk of 3D water molecules?
Inspired by David G. Stork’s post https://mathematica.stackexchange.com/a/84097/10361, I tried to have the molecules perform a random walk
...
0
votes
0answers
34 views
Multivariate AR process model fit
Is there a function in Mathematica that allows me to fit a VAR model with 4 variables?
Let's say I have the following simulated data:
...
0
votes
0answers
33 views
ARIMAProcess function: how can I use raw data sheet in ARIMAProcess?
I have a data column given by:
$$0.0000093\\
0.0000019\\
0.0000003\\
0.0000002\\
0.0000032\\
0.0000002\\\\$$
How can I use the ARIMAProcess function$[1]$ on this data sheet?
$$ * * *$$
$[1]$ https://...
1
vote
1answer
62 views
Mean of an Ito Process
I would like to compute the mean of s[t] which is given by the first equation in these coupled stochastic ordinary differential equation
...
1
vote
1answer
66 views
How to add noise to these random straight lines in 3D?
Here's a code that draws a pack of random straight lines in 3D:
...
1
vote
1answer
52 views
Implementing Random process for exponential correlation function
I'm trying to simulate a random process for a variable $-1<X(t)<1$ with average 0, i.e., $\left\langle X(t)\right\rangle =0$ and correlation $\left\langle X(t)X(0) \right\rangle \propto e^{-t/\...
0
votes
1answer
56 views
Simulation of a recursive stochastic process
I would like to simulate and plot multiple paths of the following stochastic difference equation, for any initial condition $\pi_{0} \in (0,1)$:
$\pi_{t+1} = \gamma \pi_{t}$ with probability $1/3 \pi_{...
2
votes
1answer
66 views
ItoProcess with matrix of equations
What is the cleanest/simplest way to use ItoProcess to solve the equation
$$i \text{d}\boldsymbol{\psi} = H\cdot\boldsymbol{\psi} \text{d}t + \boldsymbol{\psi}^2\...
0
votes
0answers
46 views
ItoProcess with WhiteNoiseProcess
Is there a way to use ItoProcess with a white noise process, instead of the usual WienerProcess? If I just naively use ...
2
votes
1answer
121 views
Why is ItoProcess failing here? (Stochastic Differential Equation) [closed]
Why is this code returning errors and failing to run? If I replace Abs[x[t]]^2 with just x[t] it works perfectly.
...
2
votes
1answer
70 views
RandomFunction with a QueueingProcess for more than one service handler hangs, why?
In Mathematica, I want to, say, investigate a M/M/4 queue, that is a single queue with 4 services each handling jobs from that same queue. The arrival rate is 4 and the service rate is 2. I've ...
1
vote
0answers
37 views
Generalize WienerProcess
Together the WhiteNoiseProcess, which includes the option of specifying a specific distribution for the noise, and the TransformProcess, which allows functions of processes, provide a great deal of ...
1
vote
0answers
53 views
0
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0answers
48 views
Correlated random variables
Assume we have a random variable $X(t)$ that changes as a function of time satisfying a correlation $\left\langle X(0) X(\tau) \right\rangle=e^{-\tau/\tau_c}$. Is Mathematica able to generate random ...
7
votes
1answer
168 views
RandomPoint inside mesh for walk-on-spheres Monte Carlo PDE solver
I'm trying to understand a Monte-Carlo Laplace/Poisson PDE solver:
http://www.cs.cmu.edu/~kmcrane/Projects/MonteCarloGeometryProcessing/paper.pdf
This method inspired by random-walks and ray-tracing ...
0
votes
0answers
35 views
How can i calculate the dynamical evolution of states and a probability plot of them?
Using 4 correlation matrices i define as my market states i have to follow the evolution of the market as dynamical transitions between these states. In other words, i have to show the evolution ...
14
votes
1answer
219 views
Ito Process sourced by Gaussian Process?
Question
Is it possible to extend the function ItoProcess so that it takes correlated noise?
I.e would like to be able to write
...
2
votes
0answers
47 views
How is a Lévy stabile process pdf normalized?
I'm interested in how to deal with α-stabile probability density functions, for example one with the Laplace image like:
$ \phi(s) = s^{(\alpha-1)}*e^{-\nu s^{\alpha}} $
I can work with this ...
3
votes
1answer
203 views
Fast way of re-ordering list
I have a list which at each iteration of my algorithm is being modified. What I want to do is to find the elements that satisfy certain criterion (below it's simply being above the neighborhood ...
3
votes
1answer
204 views
Connecting 2 graphs according to NearestNeighbor and degree distribution
Context and example:
Suppose we have 2 graphs $g_1,g_2$ that we connect together by introducing edges between each node of $g_1$ and its corresponding nearest neighbors within the second graph $g_2.$ ...
0
votes
2answers
80 views
Need to calculate total distance traveled in a 2D random walk
Part1
s = {0., 0.};
path = Table[s += RandomReal[{-0.5, 0.5}, 2], {100}];
ListLinePlot[path, ImageSize -> Small]
path
This part of the code generates 100 xy ...
0
votes
3answers
427 views
How can I generate monotonic random real numbers
My question is simple, and therefore I made a search of an answer to it using the Repository of this forum. There are relevant questions, however, none of them answers to the following question.
My ...
1
vote
0answers
26 views
RandomFunction of the InhomogeneousPoissonProcess: unexpected behavior
For a $ 100 000 $ realization of the inhomogenous Poisson random process
...
3
votes
0answers
24 views
Fix parameter in EstimateProcess
Can I fix some parameter in EstimateProcess?
I want to estimate the transition matrix of a hidden markov process without optimization/change of the distribution ...
1
vote
2answers
46 views
Generating random variates inside summation
I'd like to generate a table of sums which each a non-correlated, normally distributed random variate inside. Here is the sample code:
...
3
votes
1answer
150 views
Reverse graph generation
The more usual way of generating graphs and random graphs, is to start from a mechanism of adding nodes (e.g. randomly embedding or connecting, or randomly rewiring edges, etc), and for which we know ...
1
vote
0answers
61 views
Simulating Stochastic Matrix Differential Equation with Arbitrary Autocorrelation Function
I want to numerically simulate a matrix differential equation that includes a stochastic (vector) Gaussian noise $\mathbf{n}$, where the different vector components are independent, and each component ...
2
votes
1answer
97 views
Combine WienerProcess and WhiteNoiseProcess
I'm trying to simulate an IMU (inertial measurement unit) using a simple model:
$$
\tilde a(t) = a(t) + b(t) + c(t)
$$
where $\tilde a$ is the measured value, $a$ is the true value, $b$ is the ...
1
vote
1answer
127 views
How to generate Markov chains with given length and end state?
Suppose I have a discrete Markov process with states called 'Alice', 'Bob', 'Charlie', 'Daryl', 'Edith', and 'Fiona' and a given transition matrix. How can I get Mathematica to generate a finite ...
2
votes
1answer
291 views
Monte Carlo Simulation of a Double Well Potential (Edited)
I am looking for a possible way to simulate the temperature effect on a collection of atoms sitting within a double well potential, say something like
...
0
votes
1answer
430 views
Adding white noise to a signal of two variables
When a signal depends on two variables, e.g.,
f[k1_, k2_] :=
Exp[I 0.75 (k1 + 0.3 k2)] + 1.5 Exp[I (0.2 k1 + 0.3 k2)] + Exp[I (0.2 k1 + 0.4 k2)];
where ...
7
votes
5answers
1k views
Survival Probability for Random Walks
The Survival Probability for a walker starting at the origin is defined as the probability that the walker stays positive through n steps. Thanks to the Sparre-Andersen Theorem I know this PDF is ...
9
votes
1answer
287 views
Modelling snowfall as a random walk with a drift
I am trying to simulate a (very) simple model of snow fall/accumulation using random walks in the following way:
...
3
votes
1answer
368 views
Generate Gaussian process with squared exponential covariance function
In a (stationary) Gaussian Process, values which are closeby are more similar than values far away from each other. The correlation function tends to zero as distance increases. Often, one models the ...
7
votes
2answers
327 views
Record Statistics for Discrete Random Walks
I code a random walk of length 100 drawn from a LaplaceDistribution:
Accumulate[RandomVariate[LaplaceDistribution[0, 1], 10000]]
I am having trouble counting the ...
5
votes
1answer
142 views
Driving a system of differential equations with an AR1-Process
I have the following system of differential equations:
...
0
votes
0answers
105 views
Non-Gaussian random field generation
I would like to generate a height field that has a user specified distribution
of slopes. Generating a random field with Gaussian slope distribution
is easy.
Is there a relatively simple way to ...
8
votes
2answers
378 views
How to simulate a random walk to randomly generated particle to another particle fixed at the center of a grid?
I am new in Mathematica, it is my first program. Many codes of diffusion-limited aggregation are available but, they are too difficult to understand.
I basically want to create a simulation of the ...
4
votes
3answers
603 views
How do I create a random point on the surface of a cube? [duplicate]
How do I create a random point on the surface of a cube? I mean on one of its six faces at random.
2
votes
1answer
157 views
Simulation of the stochastic system
I have the stochastic system which consists of 4 nonlinear equations. White Gaussian noise is used in the third equation only. Nevertheless, the whole system is stochastic.
Some problems arise when I ...
3
votes
1answer
117 views
How to plot more paths to this SDE simulation? [duplicate]
I have the following code that simulates an Ito process in Mathematica,
...
3
votes
1answer
120 views
Generating the cumulative distribution function (CDF) of a tuple made by RandomFunction
I use the RandomFunction to generate a continuous random function (trying to model a rough surface):
...
5
votes
1answer
472 views
How to use some other driving process than the WienerProcess?
According to the following reference page
http://reference.wolfram.com/language/ref/ItoProcess.html
The driving process dproc can be any process that can be converted to
a standard Ito process
...
6
votes
1answer
1k views
ItoProcess function
While looking in the help manual of Mathematica concerning the ItoProcess function I found the following:
ItoProcess[{a,b,c},x,t]: represents an Ito Process y(t)=c(t,x(t)), where dx(t)=a(t,x(t))dt+b(...
