Brownian motion is a stochastic process, continuous in space and time, used in several domains in physics. It is the motion followed by a point which velocity is a white Gaussian noise. This tag sould be used for questions concerning the properties of Brownian motion, white Gaussian noise and physical models using these concepts, like Langevin equations. It should not be used for questions about discrete random walks.
Questions tagged [brownian-motion]
258 questions
6
votes
3 answers
Is there a modern iteration of Einstein's Brownian motion theory?
I ask this question on math stackexchange but got no answer. Not sure how to move the post so I'm reposting it here.
I was arguing with my friend that Brownian motion, in the sense of a pollen moving in the fluid, could be explained by physics laws…
athos
- 405
3
votes
0 answers
Duality while studying properties of an ensemble
Was Einstein the first to propose that observing an ensemble of $N$ particles for time interval of $dt$ is same as observing a single particle of ensemble for time interval of $Ndt$?
Kutsit
- 582
2
votes
0 answers
Expected and maximum likelihood estimate positions of particle in a box
From Causal Entropic Forces, A. D. Wissner-Grossand C. E. Freer, Physical Review Letters
Regarding a particle exhibiting brownian motion within a box...
...In contrast, if the particle had merely diffused from its given
initial state, while its…
redcalx
- 131
0
votes
0 answers
About Particle Density and PDF in Einstein's Paper on Brownian Motion
In Einstein's paper, he deduced that the diffusion equation is satisfied for the number of particles per unit volume ($f(x, t)$), i.e
$$\frac{\partial f}{\partial t}=D\cdot \frac{\partial ^2 f}{\partial x^2}$$
The solution of this equation for $N$…
HappyDay
- 101
0
votes
2 answers
Easiest way to roughly explain Brownian motion?
All easy explanations of Brownian motion that I have found are all totally wrong in that they just essentially say something like "motion of the pollen is being moved by individual water molecules" which in today's culture says absolutely nothing.…
user128534
- 21
0
votes
0 answers
Is brownian motion a good model for the movement of a particle in water?
I am not very knowledgable with respect to physics, I come from the math SE. I was wondering about Brownian motion and how close is the model to the phenomenon that started it all: the movement of a particle of pollen in a glass of water.
What I'm…
John Cataldo
- 101
0
votes
1 answer
What is the difference between these two equations for the probability density function of Brownian motion?
I have been seeing two different versions of the density function everywhere. One involves Dt as the diffusion coefficient:
$$
f(x) = 1/\sqrt{4πDt} \exp(-x^2/(4Dt))
$$
Whereas the other seems more standard, over here with
$$
f(x) = 1/\sqrt{2πt}…
0
votes
0 answers
Brownian motion and physical meaning
I have read Stochastic Differential Equations by Bernt Oksendal
It constructs Brownian motion by Kolmogorov extension theorem by consider $p(t,x,y)=(2\pi t)^{-n/2} e^{- \frac{|x-y|^{2}}{2t}}$
But I can't understand what is the relation to the…
user134927