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

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17
votes
1answer
302 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 ...
15
votes
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
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 ...
12
votes
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 ...
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 ...
7
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
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 ...
6
votes
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. ...
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
608 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
216 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
165 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
879 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(...
4
votes
2answers
170 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
525 views

Boundary condition for stochastic differential equation

I have a simple stochastic differential equation (SDE) with white noise: ...
4
votes
1answer
110 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
223 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
389 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
328 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
72 views

ITO Process with random initial position

I am trying to define an ITO process with random initial state but its only drawing once an uses it for all paths. Here is the code: ...
3
votes
1answer
86 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
282 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'...
3
votes
1answer
441 views
3
votes
0answers
147 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 $\left\langle\eta_k(t)\eta_j(...
3
votes
0answers
117 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
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 $$F=F(\omega)=\displaystyle\int_{0}^{T}h_{t}...
2
votes
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 ...
2
votes
1answer
162 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
119 views

Ito Process paths over a Plot3D

I was wondering if its possible to draw the simulated paths of an Ito diffusion over the probability density function. Ito Process: ...
2
votes
1answer
87 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
202 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 http://math.stackexchange.com/questions/1385633/solving-sde-fracdytdt-c-sigma-wwtyt-...
2
votes
1answer
87 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
206 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
310 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
236 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
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 ...
1
vote
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 ...
1
vote
1answer
104 views

Evaluating an ItoProcesss function

The following is my Stochastic D.E.: ...
1
vote
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 ...
1
vote
0answers
119 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 ...
1
vote
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. ...
1
vote
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: ...
0
votes
1answer
57 views

Ito process for 2D system

I have the following 2D dynamical system that I solve with NDSolve: ...
0
votes
1answer
89 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
votes
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?
0
votes
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.
0
votes
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. ...
0
votes
0answers
41 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) ...
0
votes
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 ...
0
votes
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 ...