Questions tagged [random-process]
The random-process tag has no usage guidance.
40
questions
1
vote
1answer
50 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
36 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
44 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
38 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
58 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
37 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 ...
0
votes
1answer
74 views
Why is ItoProcess failing here? (Stochastic Differential Equation)
Why is this code returning errors and failing to run? If I replace Abs[x[t]]^2 with just x[t] it works perfectly.
...
1
vote
0answers
32 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
50 views
0
votes
0answers
31 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
132 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
33 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
186 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
45 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
185 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
182 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
60 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
329 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
24 views
RandomFunction of the InhomogeneousPoissonProcess: unexpected behavior
For a $ 100 000 $ realization of the inhomogenous Poisson random process
...
3
votes
0answers
22 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
44 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
131 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
56 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
82 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
92 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
242 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
361 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
273 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
308 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
320 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
141 views
Driving a system of differential equations with an AR1-Process
I have the following system of differential equations:
...
0
votes
0answers
91 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 ...
7
votes
2answers
333 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
544 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
149 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 ...
4
votes
1answer
100 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
105 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
427 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(...
