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Stochastic process

About: Stochastic process is a research topic. Over the lifetime, 31227 publications have been published within this topic receiving 898736 citations. The topic is also known as: random process & stochastic processes.


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Journal ArticleDOI
TL;DR: It is shown that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size and the average network degree grows at least poly-logarithmically in this size.
Abstract: We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size and the average network degree grows at least poly-logarithmically in this size. We also establish finite-sample confidence bounds on maximum-likelihood blockmodel parameter estimates from data comprising independent Bernoulli random variates; these results hold uniformly over class assignment. We provide simulations verifying the conditions sufficient for our results, and conclude by fitting a logit parameterization of a stochastic blockmodel with covariates to a network data example comprising self-reported school friendships, resulting in block estimates that reveal residual structure.

274 citations

Journal ArticleDOI
TL;DR: In this article, limit distributions of extremes of a process satisfying the stochastic difference equation Y n -A n Y n−1 +B n, n⩾1,Y 0 ⩾0, where {An, Bn} are i.i.d.

274 citations

Journal ArticleDOI
J.P. Bonnet, D. R. Cole1, J. Delville, Mark Glauser1, Lawrence Ukeiley1 
TL;DR: In this article, the root mean square (RMS) velocities are computed from the estimated and original velocity fields and comparisons are made, in order to quantitatively assess the technique, and the results show that the complementary technique, which combines LSE and POD, allows one to obtain time dependent information from the POD while reducing the amount of instantaneous data required.
Abstract: The Proper Orthogonal Decomposition (POD) as introduced by Lumley and the Linear Stochastic Estimation (LSE) as introduced by Adrian are used to identify structure in the axisymmetric jet shear layer and the 2-D mixing layer. In this paper we will briefly discuss the application of each method, then focus on a novel technique which employs the strengths of each. This complementary technique consists of projecting the estimated velocity field obtained from application of LSE onto the POD eigenfunctions to obtain estimated random coefficients. These estimated random coefficients are then used in conjunction with the POD eigenfunctions to reconstruct the estimated random velocity field. A qualitative comparison between the first POD mode representation of the estimated random velocity field and that obtained utilizing the original measured field indicates that the two are remarkably similar, in both flows. In order to quantitatively assess the technique, the root mean square (RMS) velocities are computed from the estimated and original velocity fields and comparisons made. In both flows the RMS velocities captured using the first POD mode of the estimated field are very close to those obtained from the first POD mode of the unestimated original field. These results show that the complementary technique, which combines LSE and POD, allows one to obtain time dependent information from the POD while greatly reducing the amount of instantaneous data required. Hence, it may not be necessary to measure the instantaneous velocity field at all points in spacesimultaneously to obtain the phase of the structures, but only at a few select spatial positions. Moreover, this type of an approach can possibly be used to verify or check low dimensional dynamical systems models for the POD coefficients (for the first POD mode) which are currently being developed for both of these flows.

273 citations

Journal ArticleDOI
TL;DR: In this article, a random population model is proposed to predict recombination spectra, transients, and gain of quantum-dot ensembles, and the impact of a slowdown of energy relaxation is modeled.
Abstract: Carrier capture and recombination in quantum dots are random processes. Conventional rate equation models do not take into account this property. Based on our theory of random population we predict recombination spectra, transients, and gain of quantum-dot ensembles. Even with infinitely fast interlevel energy relaxation excited levels become considerably populated. The impact of a slowdown of energy relaxation is modeled and criteria for a conclusive experimental observation of a finite interlevel-scattering time are given.

273 citations

Journal ArticleDOI
TL;DR: A detailed introduction to directed transport in Brownian motors occurring in spatially periodic systems far from equilibrium is presented in this paper, which elucidates the prominent physical concepts and novel phenomena with a representative dissipative Brownian motor dynamics.
Abstract: A detailed introduction to directed transport in Brownian motors occurring in spatially periodic systems far from equilibrium is presented. We elucidate the prominent physical concepts and novel phenomena with a representative dissipative Brownian motor dynamics. Its main ingredient is a thermal noise with time-dependent temperature modulations that drive the system out of thermal equilibrium in a spatially asymmetric (ratchet-) potential. Yet, this asymmetric setup does not exhibit a concomitant obvious bias into one or the other direction of motion. Symmetry conditions for the appearance (or not) of directed current, its reversal upon variation of certain parameters, and various other generic features and applications are discussed. In addition, we provide a systematic classification scheme for Brownian motor models and review historical landmark contributions to the field.

273 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023159
2022355
2021985
20201,151
20191,119
20181,115