# 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
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### 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 ...
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### 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 ...
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### 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 ...
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 ...
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 ...
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)...
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: ...
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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### Puzzling behavior of ItoProcess with Abs

Hi I am simulating a Fisher-Wright diffusion, it works ...
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### 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 ...
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 ...
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### 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": ...
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, ...
125 views

### Stochastic Mathieu equation: Is this a numerical instability?

So I am a beginner with stochastic differential equations and came across Mathematica's capabilities for solving them. I am solving the stochastic Mathieu equation with a harmonic forcing term that ...
167 views

### Solve a System of mixed SDE and ODE

I have a system of differential equation to solve, but it's a mixed system of ODE and SDE. I'm not sure whether there is any way to solve this kind of system or not. My equations are: ...
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My code: ...
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### How to simulate two coupled birth-death-immigration processes?

I am simulating a birth-death-immigration process for two coupled populations that interact by virtue of the birth-rate in one population being equal to the death-rate in the other population. The two ...
160 views

### How to reformulate differential equation problem as OrnsteinUhlenbeckProcess

I have the following differential equation m*x''[t] + k*x'[t] - randomForce[t] == 0 which describes an oscillating particle with mass ...
219 views

### Solving a differential equation with a stochastic force term with NDSolve [duplicate]

I am asking how NDSolve can be used to solve the following differential equation, What is the correct code to solve the following differential equation ...
I have a controlled stochastic process described by $\dot{x} = X(x) + u(t) + \eta_x(t),$ where $u$ is the control, $\eta_x$ is a white noise with zero mean. The equation is called Langevin equation. ...
I want to simulate the movement of a damped single particle which vibrates due to Brownian motion. $m \ddot{x} + \gamma \dot{x} - \xi(t)=0$ where $\gamma$ is the friction constant and $\xi(t)$ a "...