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

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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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411 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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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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191 views

SDE boundary condition

I have a simple SDE with white noise: ...
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161 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. ...
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59 views

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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92 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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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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136 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 ...
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94 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.
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129 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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96 views

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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160 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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177 views

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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48 views

Determine appropriate initial conditions for exit time

These are some constants: ...