Questions tagged [random-process]
The random-process tag has no usage guidance.
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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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answer
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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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3
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3
answers
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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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2
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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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1
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294
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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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1
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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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1
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1
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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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1
answer
100
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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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1
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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.$ ...
user52181
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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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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 ...
user52181
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0
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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
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1
answer
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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 ...
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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 ...
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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
...
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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 ...
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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 ...
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1
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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:
...
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4
votes
1
answer
412
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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 ...
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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 ...
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1
answer
148
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Driving a system of differential equations with an AR1-Process
I have the following system of differential equations:
...
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112
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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 ...
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406
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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 ...
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651
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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.
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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 ...
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How to plot more paths to this SDE simulation? [duplicate]
I have the following code that simulates an Ito process in Mathematica,
...
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