# 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.

341 questions
Filter by
Sorted by
Tagged with
1 vote
25 views

### Properties of random-walk in infinite and finite two-dimensional space: probability of two particles being in the same location at time t

I have been told that one of the property of the continuous-time random walk in two dimensions is that: $$\int_{Z} \, G(z, t | p_1) \, G(z, t | p_2) \,dz = \,G(p_1,p_2,2t)$$ where ...
1 vote
35 views

### Do Stochastic Differential Equation models conserve energy?

I have recently started looking into stochastic models of chemical reaction systems, particularly the Chemical Langevin Equation (CLE) SDE model (e.g. here). One thing I'm trying to understand is ...
28 views

### Where can I get a good quality video (preferably slow motion / high frame rate) of Brownian motion particles for tracking their positions?

I am trying to analyse how good the Langevin equation fits actual experimental data by tracking the position of Brownian motion particles from video footage. However, I was unable to get my hands on a ...
54 views

44 views

### Fokker-Planck: uniqueness and convergence to stationary distribution

Consider the Langevin equation ($N$-dimensional) with nonlinear drift term, but expressible as a gradient of a function $U(\vec{x})$. Namely, consider the stochastic process described by the set of ...
74 views

### Meaning of $\langle X(t')X(t'') \rangle$?

Context My background is not in physics so I am not very familiar with the $\langle \rangle$ notation. I am trying to understand the following in a paper that I am reading (Berglund AJ., PhysRevE., ...
1 vote
16 views

### Physical interpretation of a multi-time (more than 2) autocorrelation function: non-Gaussian diffusion

In non-equilibrium statistical mechanics, the time-autocorrelation functions become the cornerstone of various theories and models. One such important autocorrelation is the velocity autocorrelation ...
1 vote
26 views

### Regarding calculation the moments of a random variable whose probability distribution obeys the Fokker Planck equation

I was going through Van Kampen's Stochastic Processes in Physics and Chemistry, and I was trying to solve the exercises from Chapter 8 about the Fokker Planck equation (just in case context could help ...
60 views

### Cosmology context - MCMC code : Recomputation of covariance matrix after each point accepted

I am working on a MCMC code (basically with Metropolis-Hastings) and I would like to understand different important points. We always mention the covariance matrix which is used in the computation of ...
34 views

### Second-order Dirac equation

I'm wondering if one of you could tell me about the following equation: $$\partial_t \Psi = i \sigma_z m - \sigma_y k \partial_x \Psi + i \sigma_y k' \partial_{xx}\Psi$$ where $m, k,k'$ are real ...
140 views

### Is there consensus among physicists that reality is fundamentally deterministic? [duplicate]

Does Heisenberg’s Uncertainty Principle mean that the universe cannot deterministically be predicted by observers, or does it mean that the universe is inherently indeterministic, meaning that the ...
11 views

### Bells jump process on the lattice, simple example

At the moment i am reading the paper of Vink, "Quantum mechanics in terms of discrete beables". (http://www.psiquadrat.de/downloads/vink93.pdf) Here, in section III, Vink uses Bells beable ...
15 views

### Statistically stationary, periodic random process

As I understand in a statistically stationary process, the statistics are invariant under a shift in time. It is natural to assume that the statistics are periodic in a periodic random process. If ...
63 views