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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.

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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Is throwing dice a stochastic or a deterministic process?

As far as I understand it a stochastic process is a mathematically defined concept as a collection of random variables which describe outcomes of repeated events while a deterministic process is something which can be described by a set of…
Julius
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Why does a collection of radioactive atoms show predictable behaviour while a single one is highly random?

Well, we know that it is impossible to say exactly when a radioactive atom will go on decay. It is a random process. My question is why then a collection of them decays in a predictable nature (exponential decay)? Does the randomness disappear when…
Sabbir Ahmed
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Derive Poisson distribution from probability per time of event

Suppose we have a probability per time $\lambda$ that something (e.g. nuclear decay, random walk takes a step, etc.) happens. It is a known result that the probability that $n$ events happen in a time interval of length $T$, is given by the Poisson…
DanielSank
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Why is Johnson noise a Gaussian process?

Noise processes in engineering and physics are frequently assumed to be Gaussian processes. This allows use of convenient analytical techniques. The question then arises as to why natural processes are Gaussian. In particular I'd like to understand…
DanielSank
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Relation between Langevin and Fokker-Planck for exponentially correlated noise

What is the corresponding Fokker-Planck equation for, $\frac{df(t)}{dt}=-kf(t)+\zeta(t)$ where, $\zeta(t)$ is random noise? In particular, how will the Fokker-Planck equation look if $\zeta(t)$ is exponentially correlated (or coloured, see this…
nitin
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How does a virus fall down in static air?

If we drop a virus from a height, in static air, will it fall to the ground like a lead ball, a balloon, or like a virus? How will it fall to the bottom? Like a Brownian particle? It will not float in the air, as its density is higher than air. But…
MatterGauge
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Itô or Stratonovich calculus: which one is more relevant from the point of view of physics?

Langevin equation provides an example of a physical model which involves a differential equation with a stochastic term. Now, I wonder, how should one treat this? When I studied stochastic processes, I learned about Itô and Stratonovich calculus*.…
Qwertuy
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Question about a Limit of Gaussian Integrals and how it relates to Path Integration (if at all)?

I have come across a limit of Gaussian integrals in the literature and am wondering if this is a well known result. The background for this problem comes from the composition of Brownian motion and studying the densities of the composed process. So…
jzadeh
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Random Walk Randomly Reflected

Hi I am not specialist in probability so I will not be surprised if the answer for this question is just a simple consequence of well known results from the random walk theory. In this case, I will be happy if you can tell me the "magic words" to…
Leandro
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Diffusion coefficient for asymmetric (biased) random walk

I want to obtain a Fokker-Planck like equation by taking the continuous limit of a discrete asymmetric random walk. Let the probability of taking a step to the right be $p$, and the probability of taking a step to the left be $q$, with $p+q=1$. Let…
SarthakC
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Renormalization and Brownian Motion

I've been reading about the renormalization group in QFT from Peskin & Schroeder, and wanted to consolidate understanding of "irrelevant operator" by connecting it to something more intuitive, aka Brownian motion. I'd be particularly interested in…
physicsdude
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Measure of Feynman path integral

Feynman path integral for non-relativistic case is defined as: $$\int\mathcal{D}[x(t)]e^{iS/\hbar}$$ where $$\int \mathcal{D[x(t)]}=\lim_{N\rightarrow\infty}\Pi_{i=0}^{i=N}\bigg(\int_{-\infty}^{\infty}\mathrm{d}x_{i}\bigg)$$ In the course and the…
aitfel
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Stochastic process generating fractional diffusion

One way to generate Brownian motion is as follows: Define a waiting time probability distribution $\psi(t)$ and step length probability distribution $\lambda(x)$. Require also that $\langle \psi \rangle = \tau$, $\langle \lambda \rangle = 0$, and…
F. Bardamu
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Random walk recurrence term and the self-energy

Consider the "first passage problem" A random walk proceeds on a graph of connected points. On this graph, there is one "end" point $j$ meaning that if the random walker lands on this point the process ends. Suppose we wish to know the mean…
DanielSank
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Sufficient and necessary conditions on random walk to obtain standard diffusion equation

In the simplest random walk model that is generally considered, the probability of the finding the particle at time $t$ in $x$, $P(x,t)$ is given by, $$ P(x,t) = \frac{1}{2}\big[ P(x-a, t-\tau) + P(x+a, t-\tau) \big] $$ where $a$ is the fixed…
user35952
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