# Questions tagged [stochastic-calculus]

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

154 questions
Filter by
Sorted by
Tagged with
1 vote
38 views

### Is there documentation for "FeynmanKacFormula" under "ItoProcess"? [closed]

Under the command ItoProcess there are "Properties related to ItoProcess" and one is "FeynmanKacFormula". Where can I find documentation on this?...
84 views

### Difficulties in solving a system of differential equations with a matrix differential equation

I'm trying to solve a system of differential equations that looks like this: ...
142 views

98 views

### Numerically solving a SDE with Markovian switching?

Consider the reference paper: https://www.sciencedirect.com/science/article/abs/pii/S0005109821004039 How would one go about numerically solving this system? I tried for the one regime case: ...
146 views

### Extension of: Numerically solving a system of SDE's with Levy noise?

A great answer by Alex is to be found here for my original question: Numerically solving a system of SDE's with Levy noise? Now Let us perturb this system with time delays so the system is: \begin{...
54 views

### Code not getting solved by NMaximize as 1/0 is encountred

I have the following code. This code requires to solve the model with two variables to optimize the function. a1 and a2 are the variables as shown in the code ...
1 vote
64 views

### Why are there problems solving this SDE system?

Following this solution by Alex: Numerically solving a system of SDE's with Levy noise?, I tried Alex's solution for a different model: ...
434 views

### Numerically solving a system of SDE's with Levy noise?

Consider this system from the following paper titled: The long-time behaviour of a stochastic SIR epidemic model with distributed delay and multidimensional L´evy jumps https://arxiv.org/pdf/2003....
487 views

### Solving Stochastic Gross-Pitaevskii equation

I am trying to solve the Stochastic Gross-Pitaevskii equation from this paper https://arxiv.org/pdf/1409.0146.pdf. But I have no idea how to solve adding a noise term. I like to see the wave function ...
21 views

### How does MarkovProcessProperties[] calculate the “LimitTransitionMatrix” of a stochastic matrix?

How does Mathematica the function MarkovProcessProperties[] calculate the “LimitTransitionMatrix” of a stochastic matrix using Cesaro limit of a transition matrix? What is it fundamentally doing to ...
265 views

75 views

### I need to calculate the optimal value of a function involving integration

I am working on a capacity sharing problem which involves the function as the picture below. I want to calculate the derivative of the function with respect to the variable $a_1.$ The profit function ...
168 views

### How to find the supremum of a brownian motion?

I imagine this is quite simple but unable to find it, if I simulate a standard brownian motion, $(B_t)_{t \geq 0}$, with ...
190 views

### Ito process with white noise

I would like to solve following system of SDEs, dx_i[t] = f[x_i[t]]*dt + dw_i[t] where d denotes ...
95 views

### System of stochastic differential equations

Is it possible to solve numerically system of coupled non-linear differential equations with noise? The system looks like ...
139 views

### Kloeden–Platen–Schurz algorithm for SDE

RandomFunction's Method setting includes "Kloeden–Platen–Schurz" as a possibility. ...
1 vote
287 views

### Fokker-Planck equation [closed]

Is there any package for simulation of Fokker-Planck equation in Mathematica? Or, in general for stochastic differential equations? 1 vote
198 views

### Correlated random field generation

I need to generate two correlated gaussian random fields. As far as I know, this question and this other provides the means to generate a single autocorrelated process. However, I am clueless about ...
1 vote
63 views

### Stochastic noise with known propability density function

How can I generate samples for random function, which functional "probability density" is known? When I say "probability density" for random function $\xi(\mathbf{q},t)$, I mean, ...
21 views

### How to simulate a non-White Gaussian process? [duplicate]

I am trying to numerically solve a second order stochastic differential equation. Usually the noise is assumed to be Wiener Process which is white as far as I know. Is it possible to use a Random ...
1 vote
431 views

### How add noise to a differential equation?

I have a differential equation: $$\frac{dx}{dt}=\operatorname{sech}(x-1)$$ I want to add noise to it and try to solve it numerically, but it seems that I am programming something wrong, because there ...
291 views

130 views

### WhenEvent in Stochastic Differential Equation

Is there a way to add events with WhenEvent or similar when using ItoProcess? Minimal example of my problem would be to change ...
190 views

### Why is ItoProcess failing here? (Stochastic Differential Equation) [closed]

Why is this code returning errors and failing to run? If I replace Abs[x[t]]^2 with just x[t] it works perfectly. ...
248 views

### Random number in system of equations, solving using NDSolve & WhenEvent

I need to analyse the effect of random forcing on the system of coupled equations. For example, I have shown the equations below. \begin{pmatrix} x1''\\x2''\\x3''\\x4''\\x5'' \end{pmatrix} + M_{(5 \...
335 views

### How can I can plot a stochastic process? [closed]

How I can plot the following stochastic process using mathmatica
1 vote
80 views

### Mean of ItoProcess

I've defined the following ItoProcess ...
60 views

### TransformedProcess: a few questions about it

I have a couple of technical questions that, after searching the internet for hours, I have not been able to find an answer to. Mathematica's online instructions are not even addressing the issue at ...
1 vote
288 views

### Simulating a bivariate Ito process

I would like to simulate a bivariate process where the two components, say $X_1(t)$ and $X_2(t),$ which are related by the following stochastic differential equations: ...
Assume we have a random variable $X(t)$ that changes as a function of time satisfying a correlation $\left\langle X(0) X(\tau) \right\rangle=e^{-\tau/\tau_c}$. Is Mathematica able to generate random ...