# Tagged Questions

Questions about stochastic calculus in Mathematica, for example how to use ItoProcess and RandomFunction.

1answer
308 views

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

These days I'm trying to conduct a model sensitivity test which is heavily based on the Markov Chain Monte Carlo simulation approach. And I find this 'MCMC' package that can perform Markov Chain ...
3answers
1k views

### Plotting the solution of a vector stochastic differential equation

I have a vector stochastic differential equation, $$\mathrm dq = p\,\mathrm dt\qquad q(0)=0$$ $$\mathrm dp = (-q -p)\mathrm dt+\mathrm dW\qquad p(0)=10$$ This can be entered to give me the process ...
2answers
682 views

### Efficient GeometricBrownianMotionProcess Monte Carlo simulation

Following the answers in this post, I'm trying to implement something similar. If the GBM stays inside the corridor [L, U] between predefined times it should return ...
1answer
230 views

### Regime Change Stochastic Process

I would like to simulate an Ito process in which the drift and diffusion terms change after hitting a boundary for the first time. For example, a Geometric Brownian Motion X which has 0 drift and ...
2answers
1k views

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

I am looking for some simple Mathematica code to model an HMM with just a few states and an equal number of observable signals (emissions). I am hoping to generate sample paths and keep track of the ...
2answers
2k views

### Solving a stochastic differential equation

How do I solve the following simple stochastic differential equation: $$m x''[t] + \Gamma x'[t] + k x[t] = \sqrt[]{2 k_{b} T/\Gamma)} \eta[t]$$ here $\eta[t]$ is Brownian motion, i.e. Wiener ...
3answers
619 views

### Share experiences, preferably the surprising ones, with using ItoProcess

Can people please share their experiences, preferably the surprising ones, with using ItoProcess? I am a big fan of ItoProcess and have already used it for several finance-related tasks, though I ...
1answer
204 views

### Error in ARIMAProcess example

I am trying to compile the sample of ARIMAProcess of MMA here .It doesn't work.What is wrong?Could you please help?I am using exact same code. ...
1answer
1k views

### Monte Carlo simulation using geometric Brownian motion

I'm relatively new to Mathematica programming, so forgive my rather unsophisticated question: I'm trying to do a Monte Carlo simulation using geometric Brownian motion (GBM). I want to write a ...
0answers
608 views

2answers
210 views

### Stochastic problem

I have to organize a small sports league and I am puzzled on how to create the game plan. We are 8 persons playing table soccer with 2 vs. 2 matches. The idea is that each person plays once with ...
1answer
162 views

1answer
275 views

### Finding the time at which an Ito process satisfies a constraint

I want to run an Ito stochastic process. I have the following parameters ...
2answers
69 views

### Simulation of two Ito processes

I would like to simulate two processes, Ito Process "A" and Ito Process "B". What I need is to have only one path of process "B" but many paths of process "A" - however, I need all these paths of ...
1answer
104 views

### Evaluating an ItoProcesss function

The following is my Stochastic D.E.: ...
1answer
79 views

### How to define a stochastic electromagnetic field? [closed]

I would like to show the effect of a stochastic electromagnetic field on a relativistic charged particle, using a manipulate box. The field should be randomly varying in time and in space, and be ...
0answers
120 views

### How to make a parameter stochastic in a differential equation system with NDSolve?

I constructed the differential equation system below, which I solved using NDSolve. Now I need one parameter ($mu$) to be stochastic, e.g. Poisson distributed around a mean and changing slightly at ...
0answers
197 views

### Simulations with MonteCarlo and Autoregressive methods

I am trying to find the best-fit trend for my data. Here I just generated it but let's say I don't know my data trend at all. ...
0answers
76 views

### Changing GeometricBrownianMotionProcess function

Since the function GeometricBrownianMotionProcess is given by Mathematica I have some technical questions. If we consider the following example: ...
1answer
57 views

### Ito process for 2D system

I have the following 2D dynamical system that I solve with NDSolve: ...
1answer
90 views

### Why does RandomFunction return variable number of data points?

I am using the following code snippet to generate Compound Poisson process random numbers: ...
1answer
190 views

### How to define a new stochastic process which is function of another process?

I need to define a new process from for example Wiener process like $U(t)=f(W(t))$, (for example $f(x)=1+x^2$ ) and then calculate the average like $\langle U(t)U(s)\rangle$. Is it possible?
1answer
98 views

### plotting sine of a wiener process and calculating derivative

How can I plot the sine of a Wiener process and compute its derivative? I only found the WienerProcess function in mathematica (version 9), but I'm not sure how to apply it.
0answers
31 views

### Why G/G/1 Queue properties Mathematica command not working?

Dear in this command I try to compute the M/M/1 properties with different arrival and service rate along with G/G/1 with arrival and service distributions are the Pareto distributions. ...
0answers
42 views

### Stochastic proccess in mathematica using itofunction and different processes(Bernoulli and weiner)

$ds(t)=K B (t) s( t)+\alpha (\mu -s (t))+\sigma dw(t)$ Where $(\alpha ,\mu ,K,B t,\sigma ,w)$ are in order(reversion factor, mean,Random N~(0,1),BernoulliProcess(0.008), Volatility,Weiner process) ...
0answers
30 views

### Is it possible to use random initial data in StratonovichProcess or ItoProcess?

I tried the following but it doesn't seem to be working ...
0answers
245 views

### Differential equation with random variable

How can I derive analytically or compute numerically the solution to following differential equation $$dy/dt = y\cdot X\cdot (y\cdot X - g(y,X))\cdot X$$ where X is a random variable (e.g. from a ...