Questions tagged [random-process]

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53 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
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1answer
68 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
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1answer
248 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 ...
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32 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: ...
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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://...
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1answer
57 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 ...
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1answer
58 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: ...
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1answer
51 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/\...
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1answer
49 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
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1answer
61 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\...
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0answers
44 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
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1answer
114 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
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1answer
64 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 ...
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0answers
36 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 ...
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0answers
51 views

Mean of ItoProcess

I've defined the following ItoProcess ...
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0answers
43 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
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1answer
160 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 ...
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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
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1answer
211 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 ...
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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
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1answer
196 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
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1answer
201 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 $g_2.$ ...
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2answers
75 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 ...
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3answers
400 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 ...
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0answers
26 views

RandomFunction of the InhomogeneousPoissonProcess: unexpected behavior

For a $ 100 000 $ realization of the inhomogenous Poisson random process ...
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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 ...
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2answers
45 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
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1answer
148 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 ...
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0answers
59 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
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1answer
93 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
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1answer
120 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
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1answer
276 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 ...
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1answer
413 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 ...
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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
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1answer
283 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
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1answer
359 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
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2answers
324 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
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1answer
142 views

Driving a system of differential equations with an AR1-Process

I have the following system of differential equations: ...
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0answers
100 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
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2answers
369 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
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3answers
588 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
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1answer
151 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
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1answer
112 views

How to plot more paths to this SDE simulation? [duplicate]

I have the following code that simulates an Ito process in Mathematica, ...
3
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1answer
117 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
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1answer
458 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
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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(...