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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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Alternatives to the Fokker-Planck equation for deriving the probability distribution associated with Langevin dynamics

I was wondering if there are any other means of obtaining exact (or analytical approximations) of the phase space probability density for a system evolving according to Langevin dynamics. The typical approach seems to be to pass to the Fokker-Planck…
aQuarkyName
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Can the solution of the Fokker-Planck equation exhibit negative values?

Is it possible for the solution of the Fokker-Planck equation to have negative values? I am referring to the mathematical aspect, irrespective of its physical interpretation. Additionally, considering that the solution represents a probability…
Faezeh
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Stochastic resonance

I am trying to look for a stochastic resonance in a system described by Langevin equation and a periodic forcing. While I can simulate an SDE numerically I have no idea how to calculate the 'signal to noise ratio' which quantifies the stochastic…
Vip
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Underdamped vs overdamped Langevin dynamics

Overdamped Langevin dynamics: $$ \frac{dx}{dt} = -\frac{1}{\gamma} V'(x) + \sqrt{\frac{2k_B T}{\gamma}} \eta(t) $$ Underdamped Langevin: $$ m \frac{d^2x}{dt^2} = -\gamma \frac{dx}{dt} - V'(x) + \sqrt{2 \gamma k_B T} \eta(t) $$ where $\eta(t)$ is a…
iacolippo
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Derivation of Kramer's equation

For the derivation of Kramer's equation we use the multivariable Fokker-Planck equation: $$\frac{\partial P}{\partial t} = \frac{\partial (P A_{1})}{\partial x} + \frac{\partial (P A_{2})}{\partial v} +\frac{1}{2} \frac{\partial^{2} (P…
dexter
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Onrstein-Uhlenbeck Process with power-law-correlated noise

It's a copy I posted as: https://math.stackexchange.com/questions/4356212/orstein-uhlenbeck-process-with-power-law-correlated-noise Consider a noise-driven drifting system given by the Langevin Eq: $$\dot{v}+\gamma v =\xi$$ Where $v$ denotes…
prikarsartam
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Euler-Maruyama scheme

Can the Euler-Maruyama method be used to simulate Langevin equations for non-Gaussian white noise? I need to evaluate a Langevin equation of the form $$ dx= a(x)dt+D \eta dt$$ where $\eta$ is a non-Gaussian white noise.
Vip
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Mean square displacement of a Langevin equation with inertia

Consider a 1D motion of a particle $$\ddot{x}(t)=-\gamma\dot{x}(t)+\eta(t)$$ where $\langle \eta \rangle=0$ and $\langle \eta(t)\eta(t') \rangle = \tilde{D} \delta(t-t')$. How can I obtain analytically the long time asymptotic limit of the mean…
jarhead
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Waiting/jumping times of non homogeneous process on a state chain (almost Markovian)

When considering a chain of states from 0 to N in continuous time with constant up and down going transition rates, the jumping or waiting times are exponentially distributed. Now consider the following time dependent up rate and constant down…
Nicouh
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Average of a time derivative

Given a probability distribution P(x,t), we can take the average of a time-dependent quantity x(t) as \begin{equation} \overline{x(t)}=\int dx x(t) P(x,t) \end{equation} My question is: what if I have to take the average of…
J.Agusti
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Power spectrum normalization

First off, I post this question in Physics since it stems from a physics problem, but it may be more pertinent to signal processing; sorry if it's the wrong place. TLDR: what are the correct normalization factors to compare an analitycal power…
Vermis
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Why are reaction rates proportional to the the product of the reactants not their sum?

For example, if we have the following Birth-Death process Why is the differential equation describing this reaction given by Where x, y, and a are the number of the reactants (X, Y, and A respectively). The rate is always proportional to the…
M. Z.
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Probability distribution of integrated position of a two state process with jump probability

Context This problem came up in the course of thinking about the statistics of the dispersive measurement signal coming from a superconducting qubit. Such qubits have finite excited state lifetimes, typically characterized by an exponential decay…
DanielSank
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Markov processes either have stationary state or infrared collapse?

The title summarizes my question: Consider a Markov process (discrete or continuous) where the transition-step operator $P$ is independent of time and where mass/probability is conserved for some $L^1$-norm. Do these Markov processes have at least…
5th decile
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