# Questions tagged [random-process]

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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 $W_n(t)$ ...
93 views

### 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: <...
73 views

### 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 ...
97 views

### 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 ...
157 views

### 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 ...
1 vote
99 views

### 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 ...
294 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 ...
893 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
91 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
60 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, ...
76 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 ...
285 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 ...
1 vote
90 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
100 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
74 views

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1 vote
151 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 ...
358 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 ...
526 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 ...
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 ...
294 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: ...
412 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 ...
334 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 ...
148 views

### Driving a system of differential equations with an AR1-Process

I have the following system of differential equations: ...
112 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 ...
406 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 ...
651 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.