Questions tagged [random-process]
The random-process tag has no usage guidance.
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Defining function through a formula
I would like to define a cocycle on a group that maps into the unit circle. That is, I want to be able to define a function $f:G\times G\to\mathbb{T}$ such that $f(e_G,a)=f(a,e_G)=1$ for all $a\in G$ ...
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Optimization of a Markov сhain with symbolic transition rate
I am trying to work on 1D random walk that can move to left, right or stay with probabilities $p_i$,$q_i$,$r_i$ that changes with the site $i$. I am trying to simulate this by using a recurrence ...
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How to use first time generated randomly matrix? [closed]
I'm trying to solve one (very little) problem. :)
I've generated 3x3 randomly matrix with
V[i_, j_] := Table[RandomInteger[{-10i, 10j}], {3}, {3}];
Now I want to ...
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Approximate a Wiener Process by a Karhunen-Loève expansion
I'm trying to approximate a Wiener Process by a Karhunen-Loeve expansion (see slide 20) with the following code:
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Applying NDSolveValue on a differential equation
I am trying to solve stochastic Schrodinger equation (Schrodinger equation in the presence of Ornstein Uhlenbeck Process)
$$i\frac{d}{dt}\begin{pmatrix}c_1(t)\\ c_2(t)\end{pmatrix}=H(t)\begin{pmatrix}...
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Simulating a discrete time stochastic process
I would like to simulate and plot many paths of a discrete random variable $\tau_{t}$ that follows the following process:
with probability $\tau_{t-1}$, $\tau_{t}$ is either $0.6$ with probability $x$...
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How can I use RandomFunction to solve an SDE in reverse time?
I am working with a problem of the Ito-stochastic differential form given by
$$\mathrm{d}x=g(x,t)\,\mathrm{d}t+f(x,t)\,\mathrm{d}W,$$
where $W$ is a Wiener process.
I furthermore have to satisfy the ...
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I am unable to improve the (MAProcess) time series model
I am a time series novice and have been learning the art/trade from examples while being governed by the NIST handbook (ch.6, sec.4).
My question is regarding:
How to improve the estimated time ...
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Possible Bug with MultinomialDistribution
I think there is a bug in MultinomialDistribution[]. I want to generate N random variables with densities vec{p}={p1,p2,p3,...}
Of course I check that Total[vec{p}]=1 (they are densities so they sup ...
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Bad performance of 3D self-avoid persistent random walk with periodic boundary conditions
I'm trying to simulate a self-avoiding persistent random walk with periodic boundary conditions a large number of times. For some reason, the script I've written is extremely slow for self-avoiding ...
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Stochastic process: Understanding Ornstein Uhlenbeck Process
Recently, I have been trying to simulate a random/stochastic variable that follows Gaussian distribution and also has an exponential correlation function $\left\langle X(t)X(s)\right\rangle= e^{-\frac{...
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Solving stochastic equation
I am trying to solve, numerically, a classic stochastic Liouville's equation, namely
\begin{equation}
\frac{dA(t)}{dt} = -B(t)A(t)+ {\cal C}(t)
\end{equation}
with $B(t)=\cos(\omega t)$, and ...
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Applying Fourier Shift Theorem using Power Spectrum
I have a power spectrum $P(\omega) = 10/\omega^2$ and I want to simulate a random time-series realization of this process $f(t)$ and a time-shifted copy of that realization $f(t- \tau)$. To do this, I ...
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How to define the density of random 3D points and plot it?
The following code draws a random distribution of particles in 3D. The Manipulate box allows to change a few parameters (number of particles, size of clusters, ...). I would like to define the local ...
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How can I improve this code?
The code below is working well, but it's very slow in the Manipulate box. I know that the Do and AppendTo parts aren't very ...
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How to set Ornstein-Uhlenbeck function with deterministic, not a constant parameter [closed]
I want to calculate Mean and Variance of this equation
$$r(t) = x(t) +y(t) + k(t), r(0) = r_0,$$
$$dx(t) = -ax(t)dt + σdW_1(t), x(0) = 0,$$
$$dy(t) = -by(t)dt + ηdW_2(t), y(0) = 0,$$
Where $W_n(t)$ ...
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What is this this application of KalmanEstimator doing?
I struggle to understand the Kalman filter and the documentation for KalmanEstimator. Please help me understand the first Application on that documentation page. The code in question is copied here:
<...
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WienerProcess - estimate the expected value after `n` steps
Is there a way to adjust the estimated value of the WienerProcess after n steps?
Eg. could we evaluate the value of
...
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Problems with DiscreteUniformDistribution
DiscreteUniformDistribution does not seem to work as it should. For a very simple example, let's consider a discrete random variable with PMF given by prob(-1)=1/2 and prob(1)=1/2. First, we create ...
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Is there a way to generate a data-driven Monte Carlo sample from a histogram?
I have a vector with 50 elements. These are values of a random variable. I have represented the data as Histogram[RandomVariable1Histogram]. However, I need to ...
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Add gaussian noise to 2D Point
I implemented a program for a camera calibration in Mathematica with with prototypical data to see if my calibration works. Here I converted 3D object coordinates into 2D sensor coordinates. I have ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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
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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
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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:
...
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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/\...
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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_{...
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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\...
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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 ...
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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.
...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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
...
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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 ...
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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 ...
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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 $g_2.$ ...
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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 ...
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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 ...
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RandomFunction of the InhomogeneousPoissonProcess: unexpected behavior
For a $ 100 000 $ realization of the inhomogenous Poisson random process
...
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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 ...
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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:
...
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