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Regularization by Noise: Theoretical Foundations, Numerical Methods and Applications
Get PDFThe regularizing effects of noisy perturbations of differential equations is a central subject of stochastic analysis. Recent breakthroughs initiated a new wave of interest, particularly concerning non-Markovian, infinite dimensional, and rough-stochastic/Young-stochastic hybrid systems. The mini-workshop aimed to build on these developments by bringing together young researchers in the field. Particular emphasis was given to the connection to numerical stochastic analysis, aiming to put the regularizing effects of the noise into quantitative numeric use
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Asymptotic strong Feller property and local weak irreducibility via generalized couplings
Get PDFIn this short note we show how the asymptotic strong Feller property (ASF) and local weak irreducibility can be established via generalized couplings. We also prove that a stronger form of ASF together with local weak irreducibility implies uniqueness of an invariant measure. The latter result is optimal in a certain sense and complements some of the corresponding results of Hairer, Mattingly (2008)
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Regularization by noise and flows of solutions for a stochastic heat equation
Get PDFMotivated by the regularization by noise phenomenon for SDEs we prove existence and uniqueness of the flow of solutions for the non-Lipschitz stochastic heat equation ∂u∂t=12∂2u∂z2+b(u(t,z))+W˙(t,z), where W˙ is a space-time white noise on R+×R and b is a bounded measurable function on R. As a byproduct of our proof we also establish the so-called path--by--path uniqueness for any initial condition in a certain class on the same set of probability one. This extends recent results of Davie (2007) to the context of stochastic partial differential equations
Regularization by Noise and Flows of Solutions for a Stochastic Heat Equation
No full textMotivated by the regularization by noise phenomenon for SDEs, we prove existence and uniqueness of the flow of solutions for the non-Lipschitz stochastic heat equation ∂u∂t=12∂2u∂z2+b(u(t,z))+˙W(t,z),∂u∂t=12∂2u∂z2+b(u(t,z))+W˙(t,z),where ˙WW˙ is a space-time white noise on R+×RR+×R and bb is a bounded measurable function on RR. As a byproduct of our proof, we also establish the so-called path-by-path uniqueness for any initial condition in a certain class on the same set of probability one. To obtain these results, we develop a new approach that extends Davie’s method (2007) to the context of stochastic partial differential equations
Weak existence for SDEs with singular drifts and fractional Brownian or Levy noise beyond the subcritical regime
Get PDFWe study a multidimensional stochastic differential equation with additive
noise: where the drift is integrable in
space and time, and is either a fractional Brownian motion or an
-stable process. We show weak existence of solutions to this equation
under the optimal condition on integrability indices of , going beyond the
subcritical Krylov-R\"ockner (Prodi-Serrin-Ladyzhenskaya) regime. This extends
the recent results of Krylov (2020) to the fractional Brownian and L\'evy
cases. We also construct a counterexample to demonstrate the optimality of this
condition. Our methods are built upon a version of the stochastic sewing lemma
of L\^e and the John--Nirenberg inequality
Weak uniqueness for singular stochastic equations
Get PDFWe put forward a new method for proving weak uniqueness of stochastic equations with singular drifts driven by a non-Markov or infinite-dimensional noise. We apply our method to study stochastic heat equation (SHE) driven by Gaussian space-time white noise and multidimensional stochastic differential equation (SDE) driven by fractional Brownian motion with the Hurst index In both cases is a generalized function in the Besov space , , and for SDE it holds for ; thus, in both cases, it holds in the entire desired range of values of . This extends seminal results of Catellier and Gubinelli (2016) and Gyöngy and Pardoux (1993) to the weak well-posedness setting. To establish these results, we develop a new strategy, combining ideas from ergodic theory (generalized couplings of Hairer-Mattingly-Kulik-Scheutzow) with stochastic sewing of Lê
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