# Questions tagged [random-process]

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### How to run a for loop for RandomFunction in order to take an aggregate of trajectories to approximate the steady state?

I am trying to approximate the steady state for the given rate matrix: By using the ContinuousMarkovProcess function and the RandomFunction process. I want to implement some sort of for loop system ...
• 27
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### Compiling an ItoProcess

I am a new mathematica user. I am trying to use the Compile command to speed up my RandomFunction output. The code looks like this: ...
87 views

### Riesz fractional derivatives/Laplacian for Lévy flights?

There are pretty popular Lévy flights for diffusion with steps of infinite variance, mathematically requiring Riesz fractional derivatives, which in Fourier transform multiplies by $|k|^\alpha$. I ...
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### Joint Moments of Stochastic Process at Different Times

Suppose I have a random process defined in Mathematica, e.g. h = TelegraphProcess[a] I know you can use Mathematica to calculate different statistics like the mean,...
47 views

### 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 $a\in G$ ...
108 views

### 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 ...
• 160
1 vote
178 views

### 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 ...
• 19
185 views

### 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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• 3,416
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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 ...
• 3,416
200 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. ...
• 3,416
100 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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1 vote
54 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 ...
• 334
1 vote
90 views

### Mean of ItoProcess

I've defined the following ItoProcess ...
• 159
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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 ...
• 583
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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 ...
351 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 ...
• 23.1k
54 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 ...
• 127
291 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 ...
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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 $g_2.$ ...