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Florence Merlevède
Florence Merlevède is a French probability theorist whose research interests focus on dependent and weakly dependent random variables, including Bernstein inequalities and central limit theorems for these variables. She is a professor in the laboratory for analysis and applied mathematics at Gustave Eiffel University, associated with the research group on probability and statistics there. Merlevède earned her Ph.D. at Pierre and Marie Curie University in 1996, with a dissertation jointly supervised by Denis Bosq and Magda Peligrad. With Peligrad and Sergey Utev, she is coauthor of the book ''Functional Gaussian Approximation for Dependent Structures'' (Oxford University Press, 2019). She is on the editorial board of the journal ''Probability Theory and Related Fields''. In 2021, Merlevède was named a Fellow of the Institute of Mathematical Statistics The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the developmen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independence (probability Theory)
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two event (probability theory), events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other. When dealing with collections of more than two events, two notions of independence need to be distinguished. The events are called Pairwise independence, pairwise independent if any two events in the collection are independent of each other, while mutual independence (or collective independence) of events means, informally speaking, that each event is independent of any combination of other events in the collection. A similar notion exists for collections of random variables. M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weakly Dependent Random Variables
In probability, weak dependence of random variables is a generalization of independence that is weaker than the concept of a martingale. A (time) sequence of random variables is weakly dependent if distinct portions of the sequence have a covariance that asymptotically decreases to 0 as the blocks are further separated in time. Weak dependence primarily appears as a technical condition in various probabilistic limit theorems. Formal definition Fix a set , a sequence of sets of measurable functions \_^\in\prod_^, a decreasing sequence \_^\to0, and a function \psi\in\mathcal^2\times(\mathbb^+)^2\to\mathbb^+. A sequence \_^ of random variables is (\_^,\_,\psi)-weakly dependent iff, for all j_1\leq j_2\leq\dots\leq j_d [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernstein Inequalities (probability Theory)
In probability theory, Bernstein inequalities give bounds on the probability that the sum of random variables deviates from its mean. In the simplest case, let ''X''1, ..., ''X''''n'' be independent Bernoulli random variables taking values +1 and −1 with probability 1/2 (this distribution is also known as the Rademacher distribution), then for every positive \varepsilon, :\mathbb\left (\left, \frac\sum_^n X_i\ > \varepsilon \right ) \leq 2\exp \left (-\frac \right). Bernstein inequalities were proven and published by Sergei Bernstein in the 1920s and 1930s.J.V.Uspensky, "Introduction to Mathematical Probability", McGraw-Hill Book Company, 1937 Later, these inequalities were rediscovered several times in various forms. Thus, special cases of the Bernstein inequalities are also known as the Chernoff bound, Hoeffding's inequality and Azuma's inequality. The martingale case of the Bernstein inequality is known as Freedman's inequality and its refinement is k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Limit Theorem
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the Probability distribution, distribution of a normalized version of the sample mean converges to a Normal distribution#Standard normal distribution, standard normal distribution. This holds even if the original variables themselves are not Normal distribution, normally distributed. There are several versions of the CLT, each applying in the context of different conditions. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern form it was only precisely stated as late as 1920. In statistics, the CLT can be stated as: let X_1, X_2, \dots, X_n denote a Sampling ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gustave Eiffel University
Gustave Eiffel University () is a public university located throughout Metropolitan France. The university's namesake is French engineer, Gustave Eiffel. Gustave Eiffel University is known for its civil engineering and urban planning research. History Gustave Eiffel University was created by a French government decree, and was founded on 1 January 2020. It is the result of a merger of the École d'Architecture Marne-la-Vallée, the École des ingénieurs de la Ville de Paris, the École Nationale des Sciences Géographiques, the École Supérieure d'Ingénieurs en Électrotechnique et Électronique Paris, the French Institute of Science and Technology for Transport, Development and Networks, and the former University of Paris-Est Marne-la-Vallée. The merger was decided upon despite initial opposition of unions representing UPEM workers. Academics Gustave Eiffel University offers bachelors, vocational bachelors, and masters degrees in many fields ranging from arts and h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre And Marie Curie University
Pierre and Marie Curie University ( , UPMC), also known as Paris VI, was a public research university in Paris, France, from 1971 to 2017. The university was located on the Jussieu Campus in the Latin Quarter of the 5th arrondissement of Paris, France. UPMC merged with Paris-Sorbonne University into a new combined Sorbonne University. History Paris VI was one of the inheritors of the faculty of Sciences of the University of Paris, which was divided into several universities in 1970 after the student protests of May 1968. In 1971, the five faculties of the former University of Paris (Paris VI as the Faculty of Sciences) were split and then re-formed into thirteen universities by the Faure Law. The campus of Paris VI was built in the 1950s and 1960s, on a site previously occupied by wine storehouses. The Dean, Marc Zamanski, saw the Jussieu campus standing as a tangible symbol of scientific thought in the heart of Paris, with the Faculty of Science, set in the Latin Quarter, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magda Peligrad
Magda Peligrad is a Romanian mathematician and mathematical statistician known for her research in probability theory, and particularly on central limit theorems and stochastic processes. She works at the University of Cincinnati, where she is Distinguished Charles Phelps Taft Professor of Mathematical Sciences. Education and career Peligrad obtained her Ph.D. in 1980 from the Center of Statistics of the Romanian Academy. By 1983 she was working at the Sapienza University of Rome and by 1984 she had arrived at Cincinnati, where since 1988 she has supervised the dissertations of seven doctoral students. With Florence Merlevède and Sergey Utev, she is coauthor of the book ''Functional Gaussian Approximation for Dependent Structures'' (Oxford University Press, 2019). Recognition In 1995, Peligrad was elected as a Fellow of the Institute of Mathematical Statistics The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the develop ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory And Related Fields
'' Probability Theory and Related Fields'' is a peer-reviewed mathematics journal published by Springer. Established in 1962, it was originally named ''Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete'', with the English replacing the German starting from volume 71 (1986). The journal publishes articles on probability. The journal is indexed by ''Mathematical Reviews'' and Zentralblatt MATH. Its 2019 MCQ was 2.29, and its 2019 impact factor was 2.125. The current editors-in-chief are Fabio Toninelli (Technical University of Vienna) and Bálint Tóth (University of Bristol and Alfréd Rényi Institute of Mathematics). The journal CiteScore is 3.8 and its SCImago Journal Rank is 3.198, both from 2020. It is currently ranked 11th in the field of Probability & Statistics with Applications according to Google Scholar Google Scholar is a freely accessible web search engine that indexes the full text or metadata of Academic publishing, scholarly literature across a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Institute Of Mathematical Statistics
The Institute of Mathematical Statistics is an international professional and scholarly society devoted to the development, dissemination, and application of statistics and probability. The Institute currently has about 4,000 members in all parts of the world. Beginning in 2005, the institute started offering joint membership with the Bernoulli Society for Mathematical Statistics and Probability as well as with the International Statistical Institute. The Institute was founded in 1935 with Harry C. Carver and Henry L. Rietz as its two most important supporters. The institute publishes a variety of journals, and holds several international conference every year. Publications The Institute publishes five journals: *'' Annals of Statistics'' *'' Annals of Applied Statistics'' *'' Annals of Probability'' *'' Annals of Applied Probability'' *''Statistical Science'' In addition, it co-sponsors: * '' Electronic Communications in Probability'' * '' Electronic Journal of Probability'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Year Of Birth Missing (living People)
A year is a unit of time based on how long it takes the Earth to orbit the Sun. In scientific use, the tropical year (approximately 365 solar days, 5 hours, 48 minutes, 45 seconds) and the sidereal year (about 20 minutes longer) are more exact. The modern calendar year, as reckoned according to the Gregorian calendar, approximates the tropical year by using a system of leap years. The term 'year' is also used to indicate other periods of roughly similar duration, such as the lunar year (a roughly 354-day cycle of twelve of the Moon's phasessee lunar calendar), as well as periods loosely associated with the calendar or astronomical year, such as the seasonal year, the fiscal year, the academic year, etc. Due to the Earth's axial tilt, the course of a year sees the passing of the seasons, marked by changes in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the planet, four seasons a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Purpose: Because living persons may suffer personal harm from inappropriate information, we should watch their articles carefully. By adding an article to this category, it marks them with a notice about sources whenever someone tries to edit them, to remind them of WP:BLP (biographies of living persons) policy that these articles must maintain a neutral point of view, maintain factual accuracy, and be properly sourced. Recent changes to these articles are listed on Special:RecentChangesLinked/Living people. Organization: This category should not be sub-categorized. Entries are generally sorted by family name In many societies, a surname, family name, or last name is the mostly hereditary portion of one's personal name that indicates one's family. It is typically combined with a given name to form the full name of a person, although several give .... Maintenance: Individuals of advanced age (over 90), for whom there has been no new documentation in the last ten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
