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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Anisotropic rotation in active particles
My question comes from reading this paper, where they make a model called Active Ornstein-Uhlenbeck Particle (AOUP) by averaging rotational degrees of freedom of the typical Active Brownian Particle (...
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Formula for average fluorescence lifetime in Lakowicz and Masters "Principles of Fluorescence spectroscopy" 3th edition
Lakowicz and Masters define (pg. 99 equ.4.3) the average exited state lifetime as
$$\langle t\rangle = \frac{\int_0^\infty t I(t) dt}{\int_0^\infty I(t) dt}.$$
Here $I(t)$ is the time-dependent ...
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Relation between PT-MPO bond dimension and (conditional) quantum Markov order?
I'm learning the tensor-network formalism for process tensors (PT), and I'm trying to understand how different "memory" notions relate.
Consider a $k$-step open-system quantum process on a $...
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Mathematical rigor behind renormalization [closed]
I struggle to understand how theories that are based on renormalization can be considered mathematically rigorous. I understand how renormalization works for non-abelian theories, through loop ...
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What is the physical role of the control operator C in quantum filtering equations?
I am studying Vassili N. Kolokoltsov's paper "On the Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States" and need to understand the role of the control operator $...
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The physical meaning of the "coupling operator"
I am reading Vassili N. Kolokoltsov's paper arXiv:2505.14605, "On the Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States", and having trouble understanding the ...
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Complex systems with noise
A complex system is typically defined as a system composed of many interacting components whose collective behavior cannot be easily inferred from the behavior of the individual parts. The whole ...
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Stochastic calculus clarification
In an introductory statistical physics class, the overdamped Langevin equation was introduced as: $\frac{dx}{dt} = \frac{1}{\gamma}\xi$, where $\xi$ is the white noise representing the fluctuations. ...
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Compute probability current from stochastic path integral
I would like to compute the probability current associated with a stochastic differential equation, say
$$
\frac{\mathrm{d} X}{\mathrm{d} t}
=
v
+
\sigma \xi(t)
$$
where $v$ is a drift velocity, $\xi$ ...
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Sharp error bounds for approximating a state-dependent SDE by a constant-noise surrogate in a bounded basin with double limits
Consider the state-dependent SDE on the basin $ B_\delta = [m^* - \delta, m^* + \delta] $:
$$dM_t = b(M_t) \, dt + \sigma(M_t) \, dW_t, \qquad b(m) = -(m - \tanh(Am)), \quad \sigma(m) = \sqrt{\frac{1 -...
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How to derive Fourier-Laplace transform of random walk master equation on 2D lattice (Part 2)?
This question is linked with this question and is related to this paper.
The Fourier-Laplace transform is given by:
$$P(q,r,s)=\sum_{t=0}^{\infty}\sum_{m,n=-\infty}^{\infty}\frac{e^{iqm+irn}}{(1 + s)^{...
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How to derive Fourier-Laplace transform of random walk master equation on 2D lattice (Part 1)?
I have certain gaps in clearly understanding the derivation given in this paper. Suppose a particle moves on a 2D lattice randomly. The probability of going in any one direction outb of four available ...
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Why does a higher concentration gradient lead to faster rates of diffusion?
I was reading Fick's law. I was wondering why does a higher concentration gradient lead to faster rates of diffusion? How does having 20 particles on one side of a permeable membrane differ to another ...
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How to incorporate boundary conditions in mean field descriptions while deriving macroscopic equations from microscopic stochastic processes?
The question is linked to this question.
The microscopic stochastic processes are defined using homogeneous jump probabilities between sites. The assumption will be broken when we have physical ...
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Are mean field descriptions, where macroscopic equations are approximations of microscopic stochastic processes, not valid with boundary conditions?
I am not a physicist. However, I am looking into some diffusion dynamics for my research. I am interested in diffusion in crowded environments and for that I reading a this paper. Here to find the ...
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