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

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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 ...
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76 views

Stochastic Simulation using the Gillespie algorithm

I'm trying to reproduce the simulation with demographic stochasticity in Figure 1 from the paper entitled "Dynamical Resonance Can Account For Seasonality of Influenza Epidemics" ...
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1answer
71 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?
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70 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 ...
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2answers
779 views

Solving Stochastic differential equation

How do I solve the following simple stochastic differential equation: $$ m x''[t] + \Gamma x'[t] + k x[t] = \sqrt[]{2 kb T/\Gamma)} \eta[t] $$ here $\eta[t]$ is brownian motion , i.e. Wiener ...
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1answer
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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 ...
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1answer
88 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 ...
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221 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 ...
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106 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 ...
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722 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 ...
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95 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 ...
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242 views

solve a stochastic partial differential equation

Every example about solving a stochastic differential equation uses an ordinary differential equation (derivatives with respect to one variable), but ¿what about solving this when de function depends ...
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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 ...
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Ito process estimating in Mathematica

How can I estimate parameters of Ito process in Mathematica? I have some time-process data (for example assets) and want it to be described Heston model - vector Ito process.
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67 views

Evaluating an ItoProcesss function

The following is my Stochastic D.E.: ...
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120 views

Approximating a stochastic integral with a Wiener process

I would like some assistance to solve the following: $\sum\limits_{i=0}^{n-1} e^{-k(n\Delta t -i\Delta t)}\Delta z_i$ where $z$ is a Wiener process, $\Delta z_i = z((i+1)\Delta t)-z(i\Delta t)$. ...
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Cross-correlation in SDEs

Is it possible to derive a cross-correlation function between a stochastic variable and a state-variable in an SDE, such as for the simple model here, or better between two state variables in a two ...
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156 views

Solving stochastic master equation

Can someone help please me in solving the following stochastic master equation for the density matrix $\rho$? where $\rho$ is the density matrix, $\sigma_i$ are the pauli matrices, $dt$ is the ...
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How to implement an implicit iterative method for solving SDEs?

I wish to numerically solve the Black-Scholes SDE as follows $$ \begin{array}{lll} dX(t)&=&\mu X(t)dt+\sigma X(t)dW_t, \ \ \ 0\leq t\leq1,\\ X(t_0)&=&X(0), \end{array} $$ with the ...
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SDE boundary condition

I have a simple SDE with white noise: ...
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456 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 ...
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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 ...
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378 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 ...
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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 ...
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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. ...
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1answer
151 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. ...
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Changing GeometricBrownianMotionProcess function

Since the function GeometricBrownianMotionProcess is given by Mathematica I have some technical questions. If we consider the following example: ...
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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 ...
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405 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: $$ ...
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510 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 ...
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1answer
728 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 ...
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3answers
567 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 ...