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.
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".
In probability theory and statistics, the cumulantsκn of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution. Any two probability distributions whose moments are identical will have identical cumulants as well, and vice versa.
Harald August Bohr was a Danish mathematician and footballer. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the Nobel Prize-winning physicist Niels Bohr. He was on the Denmark national team for the 1908 Summer Olympics, where he won a silver medal.
In probability theory, the Gram–Charlier A series, and the Edgeworth series are series that approximate a probability distribution in terms of its cumulants. The series are the same; but, the arrangement of terms differ. The key idea of these expansions is to write the characteristic function of the distribution whose probability density function f is to be approximated in terms of the characteristic function of a distribution with known and suitable properties, and to recover f through the inverse Fourier transform.
Jørgen Pedersen Gram was a Danish actuary and mathematician who was born in Nustrup, Duchy of Schleswig, Denmark and died in Copenhagen, Denmark.
The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution defined on the domain [−R, R] whose probability density function f is a scaled semicircle, i.e. a semi-ellipse, centered at :
Anders Hjorth Hald was a Danish statistician. He was a professor at the University of Copenhagen from 1960 to 1982. While a professor, he did research in industrial quality control and other areas, and also authored textbooks. After retirement, he made important contributions to the history of statistics.
Alexander Philip Dawid is Emeritus Professor of Statistics of the University of Cambridge, and a Fellow of Darwin College, Cambridge. He is a leading proponent of Bayesian statistics.
Per Erik Rutger Martin-Löf is a Swedish logician, philosopher, and mathematical statistician. He is internationally renowned for his work on the foundations of probability, statistics, mathematical logic, and computer science. Since the late 1970s, Martin-Löf's publications have been mainly in logic. In philosophical logic, Martin-Löf has wrestled with the philosophy of logical consequence and judgment, partly inspired by the work of Brentano, Frege, and Husserl. In mathematical logic, Martin-Löf has been active in developing intuitionistic type theory as a constructive foundation of mathematics; Martin-Löf's work on type theory has influenced computer science.
William Fleetwood Sheppard FRSE LLM Australian-British civil servant, mathematician and statistician remembered for his work in finite differences, interpolation and statistical theory, known in particular for the eponymous Sheppard's corrections.
Sir William Palin Elderton KBE PhD (Oslo) (1877–1962) was a British actuary who served as president of the Institute of Actuaries (1932–1934). Elderton also had a very long association with the statistical journal Biometrika. In its early days he published several articles, and in 1935 he became chairman of the Biometrika Trust.
Statistics, in the modern sense of the word, began evolving in the 18th century in response to the novel needs of industrializing sovereign states.
The following is a timeline of probability and statistics.
Ludvig Henrik Ferdinand Oppermann was a Danish mathematician and philologist who formulated Oppermann's conjecture on the distribution of prime numbers.
Henry Lewis Rietz was an American mathematician, actuarial scientist, and statistician, who was a leader in the development of statistical theory. He became the first president of the Institute of Mathematical Statistics.
Steffen Lilholt Lauritzen FRS is former Head of the Department of Statistics at the University of Oxford and Fellow of Jesus College, Oxford, and currently Emeritus Professor of Statistics at the University of Copenhagen. He is a leading proponent of mathematical statistics and graphical models.
The cluster-expansion approach is a technique in quantum mechanics that systematically truncates the BBGKY hierarchy problem that arises when quantum dynamics of interacting systems is solved. This method is well suited for producing a closed set of numerically computable equations that can be applied to analyze a great variety of many-body and/or quantum-optical problems. For example, it is widely applied in semiconductor quantum optics and it can be applied to generalize the semiconductor Bloch equations and semiconductor luminescence equations.
