# Tag Info

Accepted

### Efficient way to simulate thousands of Markov chains

While the other answers focus on circumventing the simulations, I focus on how to speed up the simulations themselves. (Sometimes, simulations might be unavoidable.) In this situation, when calling <...
Accepted

### How to implement Markov Chain Monte Carlo with built-in functions?

As of Version 11.3, there is an undocumented utility package, called StatisticsMCMC I came to know of it from the example notebook of this repository by @...
• 326

### Efficient way to simulate thousands of Markov chains

I essentially derive a second distribution - without a need for stochastic modelling - from DiscreteMarkovProcess timeslices according to your state to value ...
• 18.6k

### Efficient way to simulate thousands of Markov chains

In general, Mathematica is not always the best tool for this type of simulation. That said, you do not need to compute sample paths to compute the mean or variance. For a Markov chain with ...

### Mathematica code for hidden Markov models (HMM)

Mathematica V10 introduced the following two functions: - HiddenMarkovProcess - FindHiddenMarkovStates Examples of their ...
• 8,698

### How can I remove a stochastic trend from a time series

I am having some troubles with removing a stochastic trend from a time series on Mathematica. It is not clear to me what exactly "removing a stochastic trend" means. If we assume "difference-...
• 37.2k
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### Optimization of the following code

The function $x \mapsto P_x([a,b])$ is continuous and piecewise linear, so it can be easily and exactly integrated with the trapezoidal rule. Then the resulting quadrature rule can be compiled for ...
Accepted

### Can built-in functions deal with stochastic delay differential equations (SDDE)?

For numerical model we can define RandomFunction[] with WienerProcess[] outside of NDSolve ...
• 41.1k
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### Numerically solving a system of SDE's with Levy noise?

To simulate Levy jumps we can use numerical model described in the paper Analysis of a stochastic SEIS epidemic model with the standard Brownian motion and Lévy jump. In this model we use ...
• 41.1k
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### ItoProcess for stochastic reaction-diffusion equation

Here's a solution following @acl's suggestion of discretizing in space. I added a diffusion coefficient d and used reflecting boundary conditions. ...
• 19.3k
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### Continuous noise representation

For white noise, you can use WhiteNoiseProcess. This is just a process, so you need to pass it to RandomFunction to get actual ...
• 136

### How to solve a stochastic differential equation?

Something like this? ...
• 11.9k
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### Find PDF of a stochastic process

For simple processes this can be done by using the function PDF: ...
• 21.6k
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### How to reformulate differential equation problem as OrnsteinUhlenbeckProcess

One could do: ...
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### Ito Process paths over a Plot3D

Using the code as in the OP, slightly modified: ...
• 22.7k

### ItoProcess for 3 coupled SDEs sourced by 5 Wiener processes

The typographic error is in the definition of the matrix ...
• 22.5k
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### Stochastic process, Corelation function, Numerical solution, real data

Sample CorrelationFunction is a biased estimator. It works better when applied to the whole ensemble of paths instead of calculating it pathwise and taking means. ...
• 808

### How to implement Markov Chain Monte Carlo with built-in functions?

I'm currently implementing a MCMC in Mathematica. What I've done so far. 1.-Build your Model 2.-Import your data (X,Y,σ) 3.-Assign the initial parameters (P1=1 and P2=2) for example. 4.-Sample ...
• 1,022
Accepted

### Solving a stochastic dynamical system

A few things: 1) The second equation doesn't match the ODEs as noted by @b.gatessucks. 2) You need to use \[DifferentialD]t on the right hand sides. 3) ...
• 19.3k
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### ITO Process with random initial position

I don't believe this is directly possible - the process is evaluated before the random paths are generated. I'll ponder further, but if you want the same effect, try something like this: ...
• 25.5k

### Hypergeometric function with a matrix argument

You can use the new in M9 function MatrixFunction to do this. For instance: ...
• 129k
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### Random Variable in Recurrence Function

You can avoid pre-evaluation with the following definition ...
• 43.5k
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### Build a histogram from stochastic data

When requiring details information for many built in "data types" that are represented graphically by a gray box (e.g., TemporalData or ...
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### Defining stochastic differential equations and simulating a system of three SDEs

Two things: 1) You can't use {} to group terms as in your z equation. See, for example, here for more info. 2) You need to ...
• 19.3k
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### Ito Process with Piecewise

Try this with UnitStep and a numeric value for V0: ...

### Ito Process sourced by Gaussian Process?

It is not a solution, but some comparison two different approach to the same problem (oscillator with random force). What we expecting from ItoProcess in this case? ...
• 41.1k
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### How can I calculate the Allan Variance of a list of Data?

I think this does what you need: ...
• 21.6k
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### How add noise to a differential equation?

One way to make random noise over the range t = 0 to 10: ...
• 7,872
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### Stochastic process: Understanding Ornstein Uhlenbeck Process

You have different x axes. For the correlation function the x axis is 0,1,2,... And for the Table you have 0,0.1,0.2,0.3,... (Note: f is not defined, I set it to f=0.1) If we change the x axis of the ...
• 45.4k