# Questions tagged [stochastic-calculus]

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

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

How I can plot the following stochastic process using mathmatica
44 views

### Mean of ItoProcess

I've defined the following ItoProcess ...
34 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 ...
39 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: ...
28 views

### Correlated random variables

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 ...
52 views

### Having trouble moving program from python to Mathematica

I'm trying to move a Covid-19 model programmed in python to Mathematica and I can't figure out how to translate this segment of the code to Mathematica. ...
50 views

### 3D Plotting for the solution of stochastic differential equation

I have the following solution of the SDE: $$U(x,t)=-6+12 * \tanh \left[x+\left(B(t)-\frac{t^{2}}{2}\right)+\int_{0}^{t} e^{s^{2}} d s\right]^{2}$$ Where $B(t)$ is white noise. In the following code ...
692 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 Ito's ...
94 views

### Driving a stochastic spiral by a velocity Brownian motion

I want to obtain the position x[t], solution of dx/dt=v and v the Orstein-Ulhenbeck process and use this x[t] in the cartesian coordinate definition of a stochastic spiral x_1(t)=tcos(t+x(t)) , x_2(t)...
168 views

### Ito Process sourced by Gaussian Process?

Question Is it possible to extend the function ItoProcess so that it takes correlated noise? I.e would like to be able to write ...
29 views

### Explosion of solution with NDSolve

I'm trying to solve a delayed ODE involving white noise with the help of NDSolve. This provides a reasonable solution for times between 0 and 20000. After that the solution seems to explode. A curious ...
81 views

### ItoProcess for 3 coupled SDEs sourced by 5 Wiener processes

Context I am trying to solve a stochastic equation corresponding to Vector resonant relaxation (the way orbital planes of stars diffuse near the galactic center, see below). Setup Within the ...
121 views

### Kolmogorov backward PDE with boundary conditions

I am trying to solve numerically Kolmogorov backward PDE with boundary conditions: ...
109 views

### Find PDF of a stochastic process

I consider the following Ito process ...
62 views

### Problem with iterations of Prepend/While

I am doing some work with black-scholes and am trying to find random interest rates based on some given information. This is my original code: ...
1k views

### Boundary condition for stochastic differential equation

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

### Expectation and direct integration give different results [closed]

I have an integral I want to compute: $\qquad \int_{\mathbb R^4} e^{-(x_1+x_2+x_3+x_4)} \left( 1-x_1-x_3 \right) dx$ To me, this should be equivalent (modulo some scaling factor) to computing the ...
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### Adding conditions to stochastic differential equations

Consider the following process ...
61 views

### Parametric Ito Process

Is it possible to make a parametric ItoProcess ? I'd like to write that equation : ...
55 views

### Ito Process with Piecewise

I have the following ItoProcess : ...
31 views

### Discrete variables in ParametricNDSolve [closed]

I'm trying to write a stochastic differential equation, using ParametricNDSolve and WhenEvents : ...
2k views

### Efficient way to simulate thousands of Markov chains

I am currently trying to simulate relaxation of a protein population while maintaining the stochastic properties of the system. For this, I used a Markov chain to describe the temporal evolution of ...
1k views

### How to implement Markov Chain Monte Carlo with built-in functions?

These days I'm trying to conduct a model sensitivity test which is heavily based on the Markov Chain Monte Carlo simulation approach. And I find this 'MCMC' package that can perform Markov Chain ...
293 views

### How can I remove a stochastic trend from a time series

I am having some troubles with removing a stochastic trend from a time series. I am carrying out a study on the US debt to GDP ratio. I noted that there's a smooth stochastic trend in the series. ...
217 views

### Defining stochastic differential equations and simulating a system of three SDEs

I am trying to work on stochastic differential equations and I have been trying to use Mathematica's built-in function to simulate the system of equations below. When i use the randomfunction to ...
64 views

### Passing the same random values for two stochastic processes

I have two Ito processes as shown below. I can define them separately, and simulate and plot them separately. The thing is, I do not want to apply RandomFunction to proc1 and proc2 separately. Because ...
157 views

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### Stability of the numerical methods for SDE

I've been figuring out with the methods for integrating of stochastic differential equations in Mathematica. I've considered the one-dimensional system: $$dx=-x dt+\sigma x dw$$ with some initial ...
364 views

### Ito Process paths over a Plot3D

I was wondering if its possible to draw the simulated paths of an Ito diffusion over the probability density function. Ito Process: ...
60 views

### How to apply TransformedProcess to a user defined ItoProcess?

Hi I would like to manipulate user defined Ito processes, say multiply my process by a deterministic function . Thanks in advance ...
79 views

### Ignoring overflows in SDE simulations

I'm trying to compute the average of the solution to an SDE by simulating some of its sample paths and then taking their Mean. The problem is my SDE is explosive ...
97 views

### Help to extend this evaluation!

I'm performing a stochastic evaluation, where i'm interested in the assymptotic behavior of the solutions, but my computer can't stand very large times. So I thought that I could evaluate a certain ...
100 views

### Build a histogram from stochastic data

I have the following code yielding my stochastic "paths": ...
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 ...
140 views

### Simulation of the stochastic system

I have the stochastic system which consists of 4 nonlinear equations. White Gaussian noise is used in the third equation only. Nevertheless, the whole system is stochastic. Some problems arise when I ...
85 views

### How to plot more paths to this SDE simulation? [duplicate]

I have the following code that simulates an Ito process in Mathematica, ...