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

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2
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1answer
215 views

SDE boundary condition

I have a simple SDE with white noise: ...
3
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0answers
223 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 ...
3
votes
0answers
421 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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0answers
49 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 ...
1
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0answers
163 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
61 views

Changing GeometricBrownianMotionProcess function

Since the function GeometricBrownianMotionProcess is given by Mathematica I have some technical questions. If we consider the following example: ...
0
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0answers
46 views

How to deal with matrices involved in system of SDEs?

This question is in continuation of the the previous posts Solving Stochastic differential equation and Fast Simulations with Compile. What I want to do is numerically solving the epidemic model which ...
0
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0answers
100 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" ...
0
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0answers
102 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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0answers
145 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 ...
0
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0answers
96 views

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.
0
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0answers
135 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, $\Delta z_i = z((i+1)\Delta t)-z(i\Delta t)$. ...
0
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0answers
169 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 ...
0
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0answers
48 views

Determine appropriate initial conditions for exit time

These are some constants: ...