Questions tagged [stochastic-calculus]

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

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1answer
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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
845 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
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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
794 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
1k 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+\...
6
votes
2answers
1k views

Boundary condition for stochastic differential equation

I have a simple stochastic differential equation (SDE) with white noise: ...
2
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1answer
170 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 ...
25
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
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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 ...
14
votes
1answer
174 views

Ito Process sourced by Gaussian Process?

Question Is it possible to extend the function ItoProcess so that it takes correlated noise? I.e would like to be able to write ...
8
votes
3answers
879 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
2answers
456 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 ...
6
votes
1answer
183 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 ...
4
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1answer
710 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 ...
3
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1answer
485 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
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1answer
166 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
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0answers
61 views

How to apply TransformedProcess to a user defined ItoProcess?

Hi I would like to manipulate user defined Ito processes, say multiply my process by a deterministic function . Thanks in advance ...
1
vote
1answer
97 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
224 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 ...