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

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7
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2answers
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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 ...
4
votes
1answer
820 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 ...
4
votes
2answers
495 views

Boundary condition for stochastic differential equation

I have a simple stochastic differential equation (SDE) with white noise: ...
3
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0answers
250 views

Malliavin Derivative with Mathematica is it possible?

Is it possible to define a Malliavin calculus with Mathematica 9? Consider a random variables on the Wiener-space $\Omega=\mathcal{C}([0,1])$ of the form ...
6
votes
0answers
588 views

ItoProcess for stochastic reaction-diffusion equation

I am trying to simulate a stochastic differential equation in time and space, but I'm unsure if this can be done in Mathematica. The sde that I would like to study is: $$ ...
17
votes
1answer
251 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 ...
12
votes
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 ...
6
votes
3answers
586 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 ...
6
votes
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 ...
4
votes
2answers
149 views

Use of Ito's lemma in ItosLemma.m (or any other method in Mathematica)

This is a follow-up question on this question: Use of Ito's lemma in ItoProcess My problem is to find some method how to use Ito's lemma in Mathematica. As an example: How can I apply Ito's ...
3
votes
1answer
83 views

Random Variable in Recurrence Function

Following the previously published question, I'm looking for the solution of RecurrenceTable with explicit random variable. For example, something like ...
3
votes
1answer
262 views

Use of Ito's lemma in ItoProcess

In the documentation for the ItoProcess it says: Converting an ItoProcess to standard form automatically makes use of ...
1
vote
1answer
269 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 ...