Example of stochastic differential equations

XIn summary, the conversation is about solving a stochastic differential equation with a quadratic term and white noise. The speaker is looking for a full solution, and another person suggests using the stationary pdf of X to get the inverse gaussian distribution.
  • #1
hkour
2
0
hello to everyone,

I have a problem solving a stochastic differential equation of the form:

dX/dt=aX²+bX+c+sXn(t),

where n(t) is white noise with a mean value equal to 0 and variance equal to one.

Does anyone know the solution of this stochastic differential equation or how to solve it?

Thank you
 
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  • #2
Without that quadratic term, this would be easy, but...

Where does this come from? What exactly do you need? Do you need a full solution, or would it be good enough to predict the mean of X?
 
  • #3
the stationary pdf of X gives the inverse gaussian distribution.
I need the full solution
 

1. What is a stochastic differential equation (SDE)?

A stochastic differential equation is a mathematical model used to describe the evolution of a system over time in the presence of random noise. It combines elements of both differential equations and probability theory to model systems that are affected by random fluctuations.

2. What are some real-world examples of SDEs?

SDEs have many applications in fields such as physics, finance, biology, and engineering. Some common examples include modeling stock prices, population dynamics, and the spread of infectious diseases.

3. How do you solve an SDE?

Solving an SDE involves finding a function or set of functions that satisfy the equation and describe the behavior of the system over time. Different techniques, such as Monte Carlo simulations or numerical methods, can be used depending on the specific SDE and its parameters.

4. What is the difference between a stochastic differential equation and an ordinary differential equation?

The main difference is that an SDE includes a stochastic or random term, while an ordinary differential equation does not. This stochastic term makes the behavior of the system uncertain and adds an element of randomness to the solution.

5. How are SDEs used in scientific research?

SDEs are used extensively in scientific research to model complex systems that are affected by random fluctuations. They can provide insights into the behavior of these systems and help researchers make predictions about their future behavior.

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