# Questions tagged [stochastic-calculus]

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

90 questions
Filter by
Sorted by
Tagged with
296 views

332 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 ...
127 views

### Why does RandomFunction return variable number of data points?

I am using the following code snippet to generate Compound Poisson process random numbers: ...
427 views

348 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 ...
288 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 ...
111 views

### Evaluating an ItoProcesss function

The following is my Stochastic D.E.: ...
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 ...
319 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 ...
235 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 ...
353 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 ...
978 views

### Boundary condition for stochastic differential equation

I have a simple stochastic differential equation (SDE) with white noise: ...
274 views

807 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 ...
2k 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 ...
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 ...