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

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15
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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 ...
13
votes
2answers
660 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 ...
12
votes
1answer
212 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 ...
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
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 ...
6
votes
3answers
562 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
196 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. ...
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 ...
6
votes
0answers
574 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: $$ ...
5
votes
2answers
200 views

Solve a stochastic equation analytically

I have a function $\vec{F}_i(t)$, which is unknown, but I do know it's mean $\langle \vec{F}_i(t) \rangle = \vec{0}$ and it's variance $\langle \vec{F}_i(t) \cdot \vec{F}_j(t') \rangle = 2 k_B T ...
5
votes
1answer
139 views

How to use Tandem Queueing Network Process?

Mathematica provides QueueingNetworkProcess and QueueingProcess. However, I can't seem to figure out how to create a tandem ...
4
votes
1answer
763 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
128 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 ...
4
votes
2answers
463 views

Boundary condition for stochastic differential equation

I have a simple stochastic differential equation (SDE) with white noise: ...
4
votes
1answer
69 views

Defining stochastic differential equation & simulating a system of three SDEs

I am no expert on SDE but I've been messing around with MMA's built in functions and it makes it quite easy to do some simple simulations. I bumped into this system of equations (below) in a paper and ...
3
votes
2answers
172 views

Plot 2d-ItoProcess data in a plane

I am trying to simulate a simple 2d Ito SDE (randomly perturbed Hamiltonian system). Below is the code. ...
3
votes
3answers
291 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 ...
3
votes
1answer
276 views

Plot A Function Of A Stochastic Process

I am trying to do something very simple in Mathematica 9. I want to play around with option pricing and for that I thought it best to use the new stochastic process functionality. So, first of all I ...
3
votes
1answer
73 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
144 views

Stochastic Predator-Prey model using Gillespie's SSA

I'm trying to model the predator-prey situation using SSA. I am very new to Mathematica so my handling of matrices is probably terrible, and that's probably adding to my confusion: ...
3
votes
1answer
239 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 ...
3
votes
1answer
325 views
3
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0answers
120 views

Stochastic Schrödinger Equation

I have a stochastic coupled Schrödinger equation to solve. $$i\frac{\mathrm d X_k(t)}{\mathrm dt}=-\left(x_{k+1}(t)+x_{k-1}(t)\right)+V_k x_k(t)+\eta_k t x_k(t)$$ where ...
3
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0answers
78 views

Solve ItoProcess SDE

I specified a SDE for a random process $y(t)$ using ItoProcess is there a mathematica function that provides the analytic solution for $y(t)$? I know ...
3
votes
0answers
249 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 ...
2
votes
2answers
203 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 ...
2
votes
1answer
157 views

Expectation of GeometricBrownianMotionProcess

I am trying to compute $$\mathbb E\left[\max\left(\frac{S_{1/2}+S_1}{2}-K,0\right)\right]$$ where $K=100$ and $S_t$ is a geometric brownian motion (with $S_0=100$, drift $r=0.05$ and volatility ...
2
votes
1answer
71 views

Stochastic process, Corelation function, Numerical solution, real data

I am new in Mathematica and stochastic process too. I would like to compute (auto)correlation function from real data. So I decide try/test Mathematica script on ...
2
votes
1answer
170 views

Solving SDE: $\frac{dy(t)}{dt}=(c+\sigma_wW(t))y(t)+\epsilon(t) $ in Mathematica

I want to solve this differential equation $\frac{dy(t)}{dt}=(c+\sigma_w W(t))y(t)+\epsilon(t) $. For details see ...
2
votes
1answer
78 views

How to obtain SliceDistribution or StationaryDistribution for an ItoProcess when it is known to exist?

According to this reference page StationaryDistribution[proc] represents the stationary distribution of the process proc, when it exists. When I define the OrnsteinUhlenbeckProcess by the ...
2
votes
1answer
171 views

How to use some other driving process than the WienerProcess?

According to the following reference page http://reference.wolfram.com/language/ref/ItoProcess.html The driving process dproc can be any process that can be converted to a standard Ito process ...
1
vote
2answers
298 views

Problem in simulating discrete time stochastic

I have been playing with some stochastic questions and specially the problem here.It seems no matter for the first time in bet, gambler is going to lose the first bet.Am I right?How can we correct the ...
1
vote
1answer
197 views

ItoProcess for coupled SDEs

I am trying to create an ItoProcess from the following system of SDEs: $\begin{bmatrix} \mathrm d x\\\mathrm d y\end{bmatrix} = \begin{bmatrix} 0 & 1\\ 0 & \theta\end{bmatrix} \begin{bmatrix} ...
1
vote
1answer
266 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 ...
1
vote
1answer
96 views

Evaluating an ItoProcesss function

The following is my Stochastic D.E.: ...
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0answers
75 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 ...
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0answers
191 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. ...
1
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0answers
74 views

Changing GeometricBrownianMotionProcess function

Since the function GeometricBrownianMotionProcess is given by Mathematica I have some technical questions. If we consider the following example: ...
0
votes
1answer
82 views

Why does RandomFunction return variable number of data points?

I am using the following code snippet to generate Compound Poisson process random numbers: ...
0
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1answer
164 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?
0
votes
1answer
70 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.
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0answers
15 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 ...
0
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0answers
135 views

System stochastic nonlinear differential equation, Ito process?

I'm trying to solve a system of nonlinear stochastic differential equation. It is a discrete nonlinear schrodinger system of n equation, with n independet weiner process. I'm actually using the Ito ...
0
votes
0answers
220 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 ...
0
votes
0answers
219 views

Time series (stochastic process) estimating parameters using characteristic function

I have a time series of assets ${A_1, A_2, ..., A_n}$, which is described by a sophisticated distribution having the following characteristic function: $\phi(u; t;\theta)$, where $\theta$ is a vector ...