Related Research Articles
In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a sequence of random variables in a probability space, 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.
In mathematics, the Wiener process is a real-valued continuous-time stochastic process named in honor of American mathematician Norbert Wiener for his investigations on the mathematical properties of the one-dimensional Brownian motion. It is often also called Brownian motion due to its historical connection with the physical process of the same name originally observed by Scottish botanist Robert Brown. It is one of the best known Lévy processes and occurs frequently in pure and applied mathematics, economics, quantitative finance, evolutionary biology, and physics.
Probability is a measure of the likeliness that an event will occur. Probability is used to quantify an attitude of mind towards some proposition whose truth is not certain. The proposition of interest is usually of the form "A specific event will occur." The attitude of mind is of the form "How certain is it that the event will occur?" The certainty that is adopted can be described in terms of a numerical measure, and this number, between 0 and 1 is called the probability. Probability theory is used extensively in statistics, mathematics, science and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.
Itô calculus, named after Kiyosi Itô, extends the methods of calculus to stochastic processes such as Brownian motion. It has important applications in mathematical finance and stochastic differential equations.
Joseph Leo Doob was an American mathematician, specializing in analysis and probability theory.
Paul-André Meyer was a French mathematician, who played a major role in the development of the general theory of stochastic processes. He worked at the Institut de Recherche Mathématique (IRMA) in Strasbourg and is known as the founder of the 'Strasbourg school' in stochastic analysis.
In mathematics, classical Wiener space is the collection of all continuous functions on a given domain, taking values in a metric space. Classical Wiener space is useful in the study of stochastic processes whose sample paths are continuous functions. It is named after the American mathematician Norbert Wiener.
In mathematics, a Bessel process, named after Friedrich Bessel, is a type of stochastic process.
In mathematics, Doob's martingale inequality, also known as Kolmogorov’s submartingale inequality is a result in the study of stochastic processes. It gives a bound on the probability that a submartingale exceeds any given value over a given interval of time. As the name suggests, the result is usually given in the case that the process is a martingale, but the result is also valid for submartingales.
Jean-Michel Bismut is a French mathematician who has been a professor at the Université Paris-Sud since 1981. His mathematical career covers two apparently different branches of mathematics: probability theory and differential geometry. Ideas from probability play an important role in his works on geometry.
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.
Marc Yor was a French mathematician well known for his work on stochastic processes, especially properties of semimartingales, Brownian motion and other Lévy processes, the Bessel processes, and their applications to mathematical finance.
In probability theory a Brownian excursion process is a stochastic process that is closely related to a Wiener process. Realisations of Brownian excursion processes are essentially just realizations of a Wiener process selected to satisfy certain conditions. In particular, a Brownian excursion process is a Wiener process conditioned to be positive and to take the value 0 at time 1. Alternatively, it is a Brownian bridge process conditioned to be positive. BEPs are important because, among other reasons, they naturally arise as the limit process of a number of conditional functional central limit theorems.
In the mathematical theory of probability, Brownian meander is a continuous non-homogeneous Markov process defined as follows:
Jacques Jean-Pierre Neveu was a Belgian mathematician, specializing in probability theory. He is one of the founders of the French school of probability and statistics.
Jean Bertoin is a French mathematician, specializing in probability theory and professor at the University of Zurich.
In the mathematical theory of probability, Lenglart's inequality was proved by Èrik Lenglart in 1977. Later slight modifications are also called Lenglart's inequality.
In the theory of martingales, the Dubins-Schwarz theorem is a theorem that says all continuous local martingales and martingales are time-changed Brownian motions.
References
- ↑ Hommage à André Revuz [Homage to André Revuz] (in French), LDAR - Paris Diderot University , retrieved 23 March 2024
- ↑ "Graduate directory", ax.polytechnique.org, École Polytechnique Alumni, retrieved 23 March 2024
- ↑ Daniel Revuz at the Mathematics Genealogy Project
- ↑ Chincholle, Blandine (2014). "Archives de l'UFR de mathématiques de l'Université Paris Diderot (1965-2008)" [Archives of the Mathematics Department of the University of Paris Diderot (1965-2008)]. gouv.fr (in French). Retrieved 23 March 2024.
- ↑ Revuz, Daniel (1970). "Mesures associées aux fonctionnelles additives de Markov I". Transactions of the American Mathematical Society (in French). 148 (2): 501–531. doi:10.2307/1995386. ISSN 0002-9947 . Retrieved 23 March 2024.
- ↑ Revuz, Daniel (1970). "Mesures associées aux fonctionnelles additives de Markov II". Wahrscheinlichkeitstheorie und Verwandte Gebiete (in French). 16 (4). Springer-Verlag: 336–344. doi:10.1007/BF00535137. ISSN 1432-2064 . Retrieved 23 March 2024.
- ↑ Li, Liping; Ying, Jiangang (2015). "Bivariate Revuz Measures and the Feynman-Kac Formula on Semi-Dirichlet Forms". Potential Analysis. 42: 775–808. doi:10.1007/s11118-014-9457-y. ISSN 1572-929X . Retrieved 23 March 2024.
- ↑ Reviews of Continuous martingales and Brownian motion:
- Norris, J.R. (1991). "Continuous martingales and Brownian motion, by D. Revuz and M. Yor". The Mathematical Gazette. 75 (474). Springer: 498–498. doi:10.2307/3618671.
- Ronald, Getoor (1991). "Book Review: Continuous Martingales and Brownian Motion". Foundations of Physics. 21. Springer: 1001–1002. doi:10.1007/BF00733223.
- Durrett, Rick (1993). "Review: D. Revuz, M. Yor, Continuous Martingales and Brownian Motion". The Annals of Probability. 21 (1). Institute of Mathematical Statistics: 588–589. doi:10.1214/aop/1176989417.
- ↑ Kendall, Wilfrid S. (1992). "Continuous Martingales and Brownian Motion". Bulletin of the London Mathematical Society. 24 (4): 410–413. doi:10.1112/blms/24.4.410.
| International | |
|---|---|
| National | |
| Academics | |
| Other | |
 | This article about a French mathematician is a stub. You can help Wikipedia by expanding it. |