Questions tagged [stochastic-calculus]

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

Filter by
Sorted by
Tagged with
2
votes
1answer
467 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.
1
vote
2answers
107 views

How can I add new columns to a Table after each evaluation?

I'm interested in simulating chemical reactions with perturbations. I can simulate a given reaction using NDSolve ("rxn"} with a given added noise component ("noise1"). Due to the noise, each ...
1
vote
0answers
85 views

ItoProcess with log

I would like to use ItoProcess to simulate some paths of $r(t)$, a process that follows the sde $$d\ln\left(r\left(t\right)\right)=\left(\theta-\ln\left(r(t)\right)\...
1
vote
1answer
269 views

Continuous noise representation

I am new to stochastic processes (and actually Mathematica too) and there are many things that I still didn't fully understand yet so please forgive me if I say something wrong. What I am trying to ...
3
votes
1answer
361 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: ...
5
votes
1answer
167 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: ...
1
vote
1answer
321 views

Ito process for 2D system

I have the following 2D dynamical system that I solve with NDSolve: ...
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 ...
1
vote
1answer
189 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 ...
2
votes
2answers
615 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
0answers
224 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 ...
6
votes
1answer
181 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
votes
1answer
464 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 ...
2
votes
1answer
157 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 ...
3
votes
0answers
309 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
297 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 ...
2
votes
1answer
334 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 https://math.stackexchange.com/questions/1385633/solving-sde-fracdytdt-c-sigma-wwtyt-...
6
votes
2answers
454 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
1k views
0
votes
1answer
259 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.
13
votes
1answer
310 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 ...
3
votes
2answers
404 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. ...
5
votes
2answers
319 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
359 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 ...
1
vote
1answer
131 views

Why does RandomFunction return variable number of data points?

I am using the following code snippet to generate Compound Poisson process random numbers: ...
2
votes
1answer
462 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} ...
3
votes
4answers
823 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 ...
4
votes
1answer
689 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 ...
0
votes
1answer
428 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?
3
votes
1answer
1k 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 ...
2
votes
1answer
127 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 ...
5
votes
1answer
414 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 ...
2
votes
1answer
204 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 $\...
0
votes
0answers
354 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
297 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 ...
1
vote
1answer
113 views

Evaluating an ItoProcesss function

The following is my Stochastic D.E.: ...
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 ...
1
vote
1answer
322 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 ...
4
votes
1answer
249 views

Parallelization of the stochastic Euler scheme

I wrote a simulation to approximate the law of a stochastic differential equation via a Monte Carlo method using the stochastic Euler scheme. Then I thought, it would be a good idea to speed up ...
1
vote
2answers
356 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 ...
6
votes
2answers
1k views

Boundary condition for stochastic differential equation

I have a simple stochastic differential equation (SDE) with white noise: ...
3
votes
0answers
276 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}...
1
vote
0answers
254 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. ...
6
votes
1answer
229 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. ...
8
votes
3answers
868 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

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(...
1
vote
0answers
85 views

Changing GeometricBrownianMotionProcess function

Since the function GeometricBrownianMotionProcess is given by Mathematica I have some technical questions. If we consider the following example: ...
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 ...
2
votes
2answers
226 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 ...
10
votes
1answer
995 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+\...