# Questions tagged [stochastic-calculus]

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

89 questions
Filter by
Sorted by
Tagged with
0answers
30 views

### Simulating Stochastic Matrix Differential Equation with Arbitrary Autocorrelation Function

I want to numerically simulate a matrix differential equation that includes a stochastic (vector) Gaussian noise $\mathbf{n}$, where the different vector components are independent, and each component ...
2answers
58 views

### Cannot solve coupled stochastic differential equations and how to find correlation of solutions?

I am trying to solve the equations $x'[t] = y[t]$, $y'[t]+(w^2+4*\gamma^2)x[t]+\gamma*y[t])=B[t]$ with the initial conditions $x=0,y=v_0$ This is what I have tried. ...
1answer
67 views

### Quality of parametric 3D plot on 2D plane

I need to plot the solution of an SDE which takes its values on the plane $\{z = 1\} \subseteq \mathbb R^3$. Here is the code of a minimal working example (the solution to the SDE is just the driving ...
2answers
266 views

### Adding conditions to stochastic differential equations

Consider the following process ...
1answer
43 views

### Parametric Ito Process

Is it possible to make a parametric ItoProcess ? I'd like to write that equation : ...
1answer
34 views

### Ito Process with Piecewise

I have the following ItoProcess : ...
0answers
21 views

### Discrete variables in ParametricNDSolve [closed]

I'm trying to write a stochastic differential equation, using ParametricNDSolve and WhenEvents : ...
1answer
159 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. ...
1answer
117 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 ...
2answers
49 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 ...
0answers
34 views

### Monitoring time step manually within RandomFunction

Consider the following stochastic differential equation ...
1answer
112 views

1answer
99 views

### 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 ...
0answers
49 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 ...
2answers
69 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 ...
3answers
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 ...
1answer
87 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 ...
1answer
83 views

### Build a histogram from stochastic data

I have the following code yielding my stochastic "paths": ...
1answer
124 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 ...
1answer
61 views

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

I have the following code that simulates an Ito process in Mathematica, ...
1answer
98 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 ...
1answer
110 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: ...
0answers
126 views

My code: ...
0answers
55 views

### 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 ...
1answer
125 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 ...
0answers
153 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 ...
0answers
101 views

### An Ito process with intermediate constraints

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. ...
1answer
397 views

### NDSolve for 2d 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 "...
1answer
134 views

### ItoProcess and/or RandomFunction numerical failure for coupled SDEs

I'm trying to simulate a physical system including noise using the ItoProcess command, the system is governed by two coupled differential equations. The potential ...
0answers
62 views

### Dealing with Vector Outputs from ItoProcess, RandomProcess (Stochastic Differential Equations)

I'm modeling stochastic chemical kinetics and the ItoProcess[] function has served me well. I am trying to write an efficient code to analyze many (Paths) trajectories of several different reagents (...
2answers
340 views

### Stochastic Lotka-Volterra Predator-Prey Model

I am struggling with writing a stochastic version of Lotka-Volterra predator-prey model. This is as far as I have gotten: ...
0answers
133 views

### How to generate a fractional Brownian motion?

In Mathematica 9.0 I run the following piece of code: ...
0answers
168 views

### Estimate parameters of two correlated geometric Brownian motions

I would like estimate the parameters of the following set of Geometric Brownian Motions: $d P(t) = \mu_P P(t) d t + \sigma_P P(t) d Z_P(t)$ $d X(t) = \mu_X X(t) d t + \sigma_X X(t) d Z_X(t)$ ...
1answer
369 views

### How to solve a stochastic differential equation? [closed]

This is a stochastic differential equation, $$dx(t) = -x(t)dt + e^{(-t)} dw(t)$$ I am not able to determine the next steps to solve this equation.
2answers
99 views

### How can I add new columns to a Table after each evaluation?

I'm interested in simulating chemical reactions with perturbations. I can simulate a given reaction using NDSolve ("rxn"} with a given added noise component ("noise1"). Due to the noise, each ...
0answers
84 views