Questions tagged [stochastic-calculus]

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

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6
votes
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(...
3
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4answers
753 views

Hypergeometric function with a matrix argument

I am looking for the evaluation of a Hypergeometric function with a matrix argument as for example in Koev and Edelman or as showcased in this Wikipedia article. From what I understand from ...
15
votes
2answers
6k 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 ...
15
votes
2answers
784 views

Fast Simulations with Compile

this post relates to another post that I didn't follow up propely. If I wanted to simulate a system of stochastic proesses like the following, and loop over this run many many times would writing the ...
10
votes
1answer
904 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: $$ dN[x,t]=N[x,t](1-N[x,t])dt+\...
5
votes
2answers
979 views

Boundary condition for stochastic differential equation

I have a simple stochastic differential equation (SDE) with white noise: ...
2
votes
1answer
127 views

How to reformulate differential equation problem as OrnsteinUhlenbeckProcess

I have the following differential equation m*x''[t] + k*x'[t] - randomForce[t] == 0 which describes an oscillating particle with mass ...
24
votes
2answers
1k 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 ...
14
votes
2answers
2k 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 ...
8
votes
3answers
826 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 ...
5
votes
2answers
395 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 ...
8
votes
1answer
2k 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 ...
5
votes
1answer
163 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
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1answer
578 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 Ito's ...
2
votes
1answer
380 views

How to solve a stochastic differential equation? [closed]

This is a stochastic differential equation, $$ dx(t) = -x(t)dt + e^{(-t)} dw(t)$$ I am not able to determine the next steps to solve this equation.
2
votes
1answer
112 views

Stochastic ODE Integration problems using RandomFunction

I'm attempting to add noise to a set of ODE's with two state variables. $$\frac{dx}{dt} = 10 -(x-1)\left(1+\frac{exp\left(\frac{x-1}{5y}\right)}{50y}\right)$$ $$\frac{dy}{dt} = 2(1-y) -y\cdot exp\left(...
1
vote
1answer
88 views

Help to extend this evaluation!

I'm performing a stochastic evaluation, where i'm interested in the assymptotic behavior of the solutions, but my computer can't stand very large times. So I thought that I could evaluate a certain ...
0
votes
0answers
155 views

Solving a differential equation with a stochastic force term with NDSolve [duplicate]

I am asking how NDSolve can be used to solve the following differential equation, What is the correct code to solve the following differential equation ...