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Questions tagged [stochastic-calculus]

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

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1answer
34 views

Parametric Ito Process

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

Ito Process with Piecewise

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

Discrete variables in ParametricNDSolve [closed]

I'm trying to write a stochastic differential equation, using ParametricNDSolve and WhenEvents : ...
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1answer
112 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. ...
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1answer
80 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 ...
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2answers
44 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 ...
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0answers
24 views

Monitoring time step manually within RandomFunction

Consider the following stochastic differential equation ...
2
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1answer
70 views

Stochastic ODE Integration problems using RandomFunction

I'm attempting to add noise to a set of ODE's with two state variables. $$\frac{dx}{dt} = 10 -(x-1)\left(1+\frac{exp\left(\frac{x-1}{5y}\right)}{50y}\right)$$ $$\frac{dy}{dt} = 2(1-y) -y\cdot exp\left(...
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0answers
19 views

Puzzling behavior of ItoProcess with Abs

Hi I am simulating a Fisher-Wright diffusion, it works ...
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1answer
100 views

Solving a stochastic dynamical system

I'm attempting to add gaussian white noise into a single equation of a 2 state variable dynamical system $$\frac{dx(t)}{dt}=1-x(t)\left(1+e^{-y(t)}\right)$$ $$\frac{dy(t)}{dt}=1-y(t)\left(1+e^{\frac{x(...
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1answer
93 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 ...
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0answers
40 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 ...
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2answers
65 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 ...
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3answers
1k 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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1answer
84 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 ...
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1answer
81 views

Build a histogram from stochastic data

I have the following code yielding my stochastic "paths": ...
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1answer
121 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 ...
3
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1answer
57 views

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

I have the following code that simulates an Ito process in Mathematica, ...
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1answer
88 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 ...
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1answer
100 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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0answers
40 views

Obtaining expressions for SDE aprroximation(s)

Appreciate any insight into whether the following is possible and how it might be 'best/properly' done. MMA models quite general Ito Processes, via ItoProcess. ...
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0answers
48 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 ...
2
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1answer
114 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 ...
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0answers
124 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 ...
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0answers
91 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. ...
1
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1answer
322 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 "...
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1answer
107 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 ...
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0answers
54 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 (...
2
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2answers
287 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: ...
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0answers
116 views

How to generate a fractional Brownian motion?

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

Estimate parameters of two correlated geometric Brownian motions

I would like estimate the parameters of the following set of Geometric Brownian Motions: $d P(t) = \mu_P P(t) d t + \sigma_P P(t) d Z_P(t)$ $d X(t) = \mu_X X(t) d t + \sigma_X X(t) d Z_X(t)$ ...
2
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1answer
311 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.
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2answers
96 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 ...
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0answers
83 views

ItoProcess with log

I would like to use ItoProcess to simulate some paths of $r(t)$, a process that follows the sde $$d\ln\left(r\left(t\right)\right)=\left(\theta-\ln\left(r(t)\right)\...
1
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1answer
177 views

Continuous noise representation

I am new to stochastic processes (and actually Mathematica too) and there are many things that I still didn't fully understand yet so please forgive me if I say something wrong. What I am trying to ...
3
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1answer
303 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: ...
5
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1answer
156 views

ITO Process with random initial position

I am trying to define an ITO process with random initial state but its only drawing once an uses it for all paths. Here is the code: ...
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1answer
253 views

Ito process for 2D system

I have the following 2D dynamical system that I solve with NDSolve: ...
24
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2answers
989 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 ...
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1answer
162 views

How to define a stochastic electromagnetic field? [closed]

I would like to show the effect of a stochastic electromagnetic field on a relativistic charged particle, using a manipulate box. The field should be randomly varying in time and in space, and be ...
2
votes
2answers
459 views

Simulation of two Ito processes

I would like to simulate two processes, Ito Process "A" and Ito Process "B". What I need is to have only one path of process "B" but many paths of process "A" - however, I need all these paths of ...
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0answers
208 views

How to make a parameter stochastic in a differential equation system with NDSolve?

I constructed the differential equation system below, which I solved using NDSolve. Now I need one parameter ($mu$) to be stochastic, e.g. Poisson distributed around a mean and changing slightly at ...
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1answer
145 views

Random Variable in Recurrence Function

Following the previously published question, I'm looking for the solution of RecurrenceTable with explicit random variable. For example, something like ...
4
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1answer
356 views

Defining stochastic differential equation & simulating a system of three SDEs

I am no expert on SDE but I've been messing around with MMA's built in functions and it makes it quite easy to do some simple simulations. I bumped into this system of equations (below) in a paper and ...
2
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1answer
143 views

Stochastic process, Corelation function, Numerical solution, real data

I am new in Mathematica and stochastic process too. I would like to compute (auto)correlation function from real data. So I decide try/test Mathematica script on ...
3
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0answers
276 views

Stochastic Schrödinger Equation

I have a stochastic coupled Schrödinger equation to solve. $$i\frac{\mathrm d X_k(t)}{\mathrm dt}=-\left(x_{k+1}(t)+x_{k-1}(t)\right)+V_k x_k(t)+\eta_k t x_k(t)$$ where $\left\langle\eta_k(t)\eta_j(...
3
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0answers
274 views

Solve ItoProcess SDE

I specified a SDE for a random process $y(t)$ using ItoProcess is there a mathematica function that provides the analytic solution for $y(t)$? I know ...
2
votes
1answer
299 views

Solving SDE: $\frac{dy(t)}{dt}=(c+\sigma_wW(t))y(t)+\epsilon(t) $ in Mathematica

I want to solve this differential equation $\frac{dy(t)}{dt}=(c+\sigma_w W(t))y(t)+\epsilon(t) $. For details see https://math.stackexchange.com/questions/1385633/solving-sde-fracdytdt-c-sigma-wwtyt-...
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2answers
380 views

Use of Ito's lemma in ItosLemma.m (or any other method in Mathematica)

This is a follow-up question on this question: Use of Ito's lemma in ItoProcess My problem is to find some method how to use Ito's lemma in Mathematica. As an example: How can I apply Ito's ...