Eugene B. Seneta (born 1941) is Professor Emeritus, School of Mathematics and Statistics, University of Sydney, known for his work in probability and non-negative matrices, [1] applications and history. [2] He is known for the variance gamma model in financial mathematics (the variance gamma process). [3] He was Professor, School of Mathematics and Statistics at the University of Sydney from 1979 until retirement, and an Elected Fellow since 1985 of the Australian Academy of Science. [4] In 2007 Seneta was awarded the Hannan Medal in Statistical Science [5] [6] by the Australian Academy of Science, for his seminal work in probability and statistics; for his work connected with branching processes, history of probability and statistics, and many other areas.
In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family 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 probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs now." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). Markov processes are named in honor of the Russian mathematician Andrey Markov.
Harald Cramér was a Swedish mathematician, actuary, and statistician, specializing in mathematical statistics and probabilistic number theory. John Kingman described him as "one of the giants of statistical theory".
Applied probability is the application of probability theory to statistical problems and other scientific and engineering domains.
In the design of experiments, optimal experimental designs are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith.
Alexander Alexandrovich Chuprov (or Tschuprov) (Russian: Алекса́ндр Алекса́ндрович Чупро́в) (Mosal'sk, February 18, 1874 - Geneva, April 19, 1926) Russian Empire statistician who worked on mathematical statistics, sample survey theory and demography.
Anatoliy Volodymyrovych Skorokhod was a Soviet and Ukrainian mathematician.
Olav Kallenberg is a Swedish-American mathematician, working in all areas of probability theory. He is especially known for his work on random measures and probabilistic symmetries, and for his graduate-level textbooks and monographs. Since 2018 he is an Emeritus Professor of Mathematics at Auburn University, AL.
A hidden semi-Markov model (HSMM) is a statistical model with the same structure as a hidden Markov model except that the unobservable process is semi-Markov rather than Markov. This means that the probability of there being a change in the hidden state depends on the amount of time that has elapsed since entry into the current state. This is in contrast to hidden Markov models where there is a constant probability of changing state given survival in the state up to that time.
The variance-gamma distribution, generalized Laplace distribution or Bessel function distribution is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the gamma distribution. The tails of the distribution decrease more slowly than the normal distribution. It is therefore suitable to model phenomena where numerically large values are more probable than is the case for the normal distribution. Examples are returns from financial assets and turbulent wind speeds. The distribution was introduced in the financial literature by Madan and Seneta. The variance-gamma distributions form a subclass of the generalised hyperbolic distributions.
Patrick Alfred Pierce Moran FRS was an Australian statistician who made significant contributions to probability theory and its application to population and evolutionary genetics.
The Applied Probability Trust is a UK-based non-profit foundation for study and research in the mathematical sciences, founded in 1964 and based in the School of Mathematics and Statistics at the University of Sheffield, which it has been affiliated with since 1964.
Peter Gavin Hall was an Australian researcher in probability theory and mathematical statistics. The American Statistical Association described him as one of the most influential and prolific theoretical statisticians in the history of the field. The School of Mathematics and Statistics Building at The University of Melbourne was renamed the Peter Hall building in his honour on 9 December 2016.
Christopher Charles Heyde was a prominent Australian statistician who did leading research in probability, stochastic processes and statistics.
Harry Kesten was a Jewish American mathematician best known for his work in probability, most notably on random walks on groups and graphs, random matrices, branching processes, and percolation theory.
In the theory of stochastic processes, a part of the mathematical theory of probability, the variance gamma (VG) process, also known as Laplace motion, is a Lévy process determined by a random time change. The process has finite moments, distinguishing it from many Lévy processes. There is no diffusion component in the VG process and it is thus a pure jump process. The increments are independent and follow a variance-gamma distribution, which is a generalization of the Laplace distribution.
Steven Neil Evans is an Australian-American statistician and mathematician, specializing in stochastic processes.
Grzegorz (“Greg”) A. Rempala is a Polish-American applied mathematician who works on the theory and applications of complex stochastic systems.
Eugene A. Feinberg is an American mathematician and distinguished professor of applied mathematics and statistics at Stony Brook University. He is noted for his work in probability theory, real analysis, and Markov decision processes.
Dilip B. Madan is an American financial economist, mathematician, academic, and author. He is professor emeritus of finance at the University of Maryland.