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In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a sequence of random variables, where the index of the sequence often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance.
Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service.
Michel Pierre Talagrand is a French mathematician. Docteur ès sciences since 1977, he has been, since 1985, Directeur de Recherches at CNRS and a member of the Functional Analysis Team of the Institut de Mathématique of Paris. Talagrand was elected as correspondent of the Académie des sciences of Paris in March 1997, and then as a full member in November 2004, in the Mathematics section.
Václav Edvard "Vic" Beneš is a Czech-American, a mathematician known for his contributions to the theory of stochastic processes, queueing theory and control theory, as well as the design of telecommunications switches.
Onno Johan Boxma is a Dutch mathematician, and Professor at the Eindhoven University of Technology, known for several contributions to queueing theory and applied probability theory.
Jan Hendrik van Schuppen is a Dutch mathematician and Professor at the Department of Mathematics of the Vrije Universiteit, known for his contributions in the field of systems theory, particularly on control theory and system identification, on probability, and on a number of related practical applications.
This page lists articles related to probability theory. In particular, it lists many articles corresponding to specific probability distributions. Such articles are marked here by a code of the form (X:Y), which refers to number of random variables involved and the type of the distribution. For example (2:DC) indicates a distribution with two random variables, discrete or continuous. Other codes are just abbreviations for topics. The list of codes can be found in the table of contents.
In probability theory, a product-form solution is a particularly efficient form of solution for determining some metric of a system with distinct sub-components, where the metric for the collection of components can be written as a product of the metric across the different components. Using capital Pi notation a product-form solution has algebraic form
In queueing theory, a discipline within the mathematical theory of probability, a fork–join queue is a queue where incoming jobs are split on arrival for service by numerous servers and joined before departure. The model is often used for parallel computations or systems where products need to be obtained simultaneously from different suppliers. The key quantity of interest in this model is usually the time taken to service a complete job. The model has been described as a "key model for the performance analysis of parallel and distributed systems." Few analytical results exist for fork–join queues, but various approximations are known.
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets.
In queueing theory, a discipline within the mathematical theory of probability, a fluid queue is a mathematical model used to describe the fluid level in a reservoir subject to randomly determined periods of filling and emptying. The term dam theory was used in earlier literature for these models. The model has been used to approximate discrete models, model the spread of wildfires, in ruin theory and to model high speed data networks. The model applies the leaky bucket algorithm to a stochastic source.
In queueing theory, a discipline within the mathematical theory of probability, a fluid limit, fluid approximation or fluid analysis of a stochastic model is a deterministic real-valued process which approximates the evolution of a given stochastic process, usually subject to some scaling or limiting criteria.
Alice Guionnet is a French mathematician known for her work in probability theory, in particular on large random matrices.
Thomas G. Kurtz is an American emeritus professor of Mathematics and Statistics at University of Wisconsin-Madison known for his research contributions to many areas of probability theory and stochastic processes. In particular, Kurtz’s research focuses on convergence, approximation and representation of several important classes of Markov processes. His findings appear in scientific disciplines such as systems biology, population genetics, telecommunications networks and mathematical finance.
The Korteweg-de Vries Institute for Mathematics (KdVI) is the institute for mathematical research at the University of Amsterdam. The KdVI is located in Amsterdam at the Amsterdam Science Park.
Amber Lynn Puha is an American mathematician and educator at California State University San Marcos. Her research concerns probability theory and stochastic processes.
JinqiaoDuan is a professor of mathematics at Illinois Institute of Technology, Chicago, USA.
References
- ↑ Michel Mandjes at the Mathematics Genealogy Project
- ↑ "Curriculum vitae" (PDF). CWI Amsterdam. Retrieved May 2, 2021.
- ↑ Mandjes, Michel. "Publications". NARCIS. Retrieved May 2, 2021.
- ↑ "Eurandom – Workshop Centre in the area of Stochastics" . Retrieved 2021-05-02.
- ↑ Mandjes, Michel (2007). Large deviations for Gaussian queues : modelling communication networks. Chichester: Wiley. ISBN 978-0-470-51509-9. OCLC 181350149.
- ↑ "Queues and Lévy fluctuation theory in SearchWorks". searchworks.stanford.edu. Retrieved 2017-05-22.
