# Questions tagged [stochastic-calculus]

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

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### 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 ...
95 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 ...
88 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 ...
63 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 ...
87 views

### Kloeden–Platen–Schurz algorithm for SDE

RandomFunction's Method setting includes "Kloeden–Platen–Schurz" as a possibility. ...
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1 vote
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### 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
89 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 ...
• 115
1 vote
59 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, ...
19 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 ...
• 111
197 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 ...
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• 3,286
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### 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 ...
• 211
129 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. ...
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• 372
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### Simulating a poker win rate over time

Poker players start with a fixed bankroll (bankroll) and play with a win-rate winRate (say measured in dollars per hour) and ...
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1 vote
61 views

### Is it possible to speed up SDE simulation?

Is it possible to speed up SDE simulation in Mathematica? I am simulating a large number of Heston processes that look like the following (note this code is only a slight modification of the ...
• 43
91 views

### How to solve forward Kolmogorov birth-death equations for unspecified number of populations

I'm attempting to use a forward Kolmogorov differential equation to model a birth-death process. This is fairly trivial when there's only one population, but I'm working with an unspecified and time-...
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### Adding conditions to stochastic differential equations

Consider the following process ...
• 1,885
1 vote
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### Parametric Ito Process

Is it possible to make a parametric ItoProcess ? I'd like to write that equation : ...
• 1,225
1 vote
97 views

### Ito Process with Piecewise

I have the following ItoProcess : ...
• 1,225
1 vote