# Questions tagged [random-process]

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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 ...
1answer
215 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 ...
1answer
339 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 ...
1answer
296 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 ...
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 ...
1answer
266 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: ...
2answers
318 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 ...
1answer
141 views

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

I have the following system of differential equations: ...
0answers
87 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 ...
2answers
322 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 ...
3answers
516 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.
1answer
144 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 ...
1answer
91 views

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

I have the following code that simulates an Ito process in Mathematica, ...
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(...
1answer
417 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 ...
1answer
101 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): ...