# Questions tagged [stochastic-processes]

A stochastic process is a random process evolving with time , i.e., a time sequence representing the evolution of some system represented by a variable whose change is subject to a random variation.

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### On the definition of a stationary process

I have come across various ways one refers to a process as stationary and cannot seem to get the equivalency and the level of rigor in each of them: According to Stochastic processes in physics and ...
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### How can we interpret a system in which the probability distribution obeys the forward and the backward Fokker-Planck equation simultaneously?

For a system involving randomness, there is no longer a unique derivative and hence no longer a unique definition of velocity. But for the forward (Ito) derivative, we can find a probability ...
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### Why is the Fokker-Planck equation only valid for the forward and backward velocities but not for the flux velocity?

I noticed that the Fokker-Planck equation is often only written for the forward velocity $\vec b$ and the backward velocity $\vec b^*$: \begin{align} \partial_t \rho + \nabla (\vec b \rho) &= D \...
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### Is the continuity equation valid for a diffusion current?

On the one hand, we have the diffusion equation: \begin{align} \frac{\partial\rho}{\partial t}&=D \nabla^2 \rho \end{align} and on the other hand, we have Fick's first law: \begin{align} \vec J = ...
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### Variance of Simulated Langevin Equation

I simulated (by Matlab) the Langevin equation for optical-trapped particle in very short time "steps" And I got this white noise figure.. The question is how I can calculate the variance (or in ...