Dietrich Stoyan (born November 26, 1940, Berlin) is a German mathematician and statistician who made contributions to queueing theory, stochastic geometry, and spatial statistics.
Dietrich Stoyan (born November 26, 1940, Berlin) is a German mathematician and statistician who made contributions to queueing theory, stochastic geometry, and spatial statistics.
Stoyan studied mathematics at Technical University Dresden; applied research at Deutsches Brennstoffinstitut Freiberg, 1967 PhD, 1975 Habilitation. Since 1976 at TU Bergakademie Freiberg, Rektor of that university in 1991—1997. He became famous by his statistical research of the diffusion of euro coins in Germany and Europe after the introduction of the euro in 2002. In 2024, he criticized together with Sung Nok Chiu a wrong proof of the hypothesis that the origin of the COVID-19 pandemic was a market in Wuhan which was published in the journal Science. [1]
Dietrich Stoyan is an honorary doctor of the Technical University of Dresden (2000) and the University of Jyväskylä (2004). He was a member of the Academy of Sciences of the GDR (1990), which disappeared in 1991. At present he is a member of the Academia Europaea (since 1992), the Berlin-Brandenburg Academy of Sciences (since 2000) and the German Academy of Sciences Leopoldina (since 2002). He is also a Fellow of the Institute for Mathematical Statistics (since 1997). In 2018 he published his autobiography In two times. [2]
Qualitative theory, in particular inequalities, for queueing systems and related stochastic models. The books
report on the results. The work goes back to 1969 when he discovered the monotonicity of the GI/G/1 waiting times with respect to the convex order.
Stereological formulae, applications for marked point processes, development of stochastic models. Successful joint work with Joseph Mecke led to the first exact proof of the fundamental stereological formulae.
A book entitled "Stochastic Geometry and its Applications" reports on these results. Its 3rd edition is the key reference for applied stochastic geometry. [3]
Statistical methods for point processes, random sets and many other random geometrical structures such as fibre processes. Results can be found in the 2013 book on stochastic geometry and in the book, Fractals, Random Shapes and Point Fields by D. and H. Stoyan. (J. Wiley and Sons, Chichester, 1994).
A particular strength of Stoyan is second-order methods.
He is also the main author of the book Statistical analysis and modelling of spatial point patterns. [4] It treats the statistics of point patterns with methods of point process theory.
Stoyan is very active in demonstrating non-mathematicians and non-statisticians the potential of statistical and stochastic geometrical methods. He published many papers in journals of physics, materials science, forestry, and geology. One topic of particular interest was random packings of hard spheres. He co-organized together with Klaus Mecke conferences where physicists, geometers and statisticians met. See the books
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 statistics and probability theory, a point process or point field is a collection of mathematical points randomly located on a mathematical space such as the real line or Euclidean space. Point processes can be used for spatial data analysis, which is of interest in such diverse disciplines as forestry, plant ecology, epidemiology, geography, seismology, materials science, astronomy, telecommunications, computational neuroscience, economics and others.
Ole Eiler Barndorff-Nielsen was a Danish statistician who has contributed to many areas of statistical science.
Stereology is the three-dimensional interpretation of two-dimensional cross sections of materials or tissues. It provides practical techniques for extracting quantitative information about a three-dimensional material from measurements made on two-dimensional planar sections of the material. Stereology is a method that utilizes random, systematic sampling to provide unbiased and quantitative data. It is an important and efficient tool in many applications of microscopy. Stereology is a developing science with many important innovations being developed mainly in Europe. New innovations such as the proportionator continue to make important improvements in the efficiency of stereological procedures.
For statistics in probability theory, the Boolean-Poisson model or simply Boolean model for a random subset of the plane is one of the simplest and most tractable models in stochastic geometry. Take a Poisson point process of rate in the plane and make each point be the center of a random set; the resulting union of overlapping sets is a realization of the Boolean model . More precisely, the parameters are and a probability distribution on compact sets; for each point of the Poisson point process we pick a set from the distribution, and then define as the union of translated sets.
In mathematics, stochastic geometry is the study of random spatial patterns. At the heart of the subject lies the study of random point patterns. This leads to the theory of spatial point processes, hence notions of Palm conditioning, which extend to the more abstract setting of random measures.
David John Bartholomew was a British statistician who was president of the Royal Statistical Society between 1993 and 1995. He was professor of statistics at the London School of Economics between 1973 and 1996.
In probability theory and statistics, Campbell's theorem or the Campbell–Hardy theorem is either a particular equation or set of results relating to the expectation of a function summed over a point process to an integral involving the mean measure of the point process, which allows for the calculation of expected value and variance of the random sum. One version of the theorem, also known as Campbell's formula, entails an integral equation for the aforementioned sum over a general point process, and not necessarily a Poisson point process. There also exist equations involving moment measures and factorial moment measures that are considered versions of Campbell's formula. All these results are employed in probability and statistics with a particular importance in the theory of point processes and queueing theory as well as the related fields stochastic geometry, continuum percolation theory, and spatial statistics.
Klaus Matthes was a German mathematician, known as the founder of the theory of marked and infinitely divisible point processes. From 1981 to 1991 he was the director of the GDR Academy of Sciences' Institute of Mathematics in Berlin.
In mathematics and telecommunications, stochastic geometry models of wireless networks refer to mathematical models based on stochastic geometry that are designed to represent aspects of wireless networks. The related research consists of analyzing these models with the aim of better understanding wireless communication networks in order to predict and control various network performance metrics. The models require using techniques from stochastic geometry and related fields including point processes, spatial statistics, geometric probability, percolation theory, as well as methods from more general mathematical disciplines such as geometry, probability theory, stochastic processes, queueing theory, information theory, and Fourier analysis.
In probability and statistics, point process notation comprises the range of mathematical notation used to symbolically represent random objects known as point processes, which are used in related fields such as stochastic geometry, spatial statistics and continuum percolation theory and frequently serve as mathematical models of random phenomena, representable as points, in time, space or both.
In probability and statistics, a point process operation or point process transformation is a type of mathematical operation performed on a random object known as a point process, which are often used as mathematical models of phenomena that can be represented as points randomly located in space. These operations can be purely random, deterministic or both, and are used to construct new point processes, which can be then also used as mathematical models. The operations may include removing or thinning points from a point process, combining or superimposing multiple point processes into one point process or transforming the underlying space of the point process into another space. Point process operations and the resulting point processes are used in the theory of point processes and related fields such as stochastic geometry and spatial statistics.
In probability and statistics, a moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. Moment measures generalize the idea of (raw) moments of random variables, hence arise often in the study of point processes and related fields.
In probability and statistics, a factorial moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. Moment measures generalize the idea of factorial moments, which are useful for studying non-negative integer-valued random variables.
In probability and statistics, a spherical contact distribution function, first contact distribution function, or empty space function is a mathematical function that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. More specifically, a spherical contact distribution function is defined as probability distribution of the radius of a sphere when it first encounters or makes contact with a point in a point process. This function can be contrasted with the nearest neighbour function, which is defined in relation to some point in the point process as being the probability distribution of the distance from that point to its nearest neighbouring point in the same point process.
In probability theory, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is also called a Poisson random measure, Poisson random point field and Poisson point field. When the process is defined on the real number line, it is often called simply the Poisson process.
In probability and statistics, a nearest neighbor function, nearest neighbor distance distribution, nearest-neighbor distribution function or nearest neighbor distribution is a mathematical function that is defined in relation to mathematical objects known as point processes, which are often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both. More specifically, nearest neighbor functions are defined with respect to some point in the point process as being the probability distribution of the distance from this point to its nearest neighboring point in the same point process, hence they are used to describe the probability of another point existing within some distance of a point. A nearest neighbor function can be contrasted with a spherical contact distribution function, which is not defined in reference to some initial point but rather as the probability distribution of the radius of a sphere when it first encounters or makes contact with a point of a point process.
Adrian John Baddeley is a statistical scientist working in the fields of spatial statistics, statistical computing, stereology and stochastic geometry.
Rouben V. Ambartzumian is an Armenian mathematician and Academician of National Academy of Sciences of Armenia. He works in Stochastic Geometry and Integral Geometry where he created a new branch, combinatorial integral geometry. The subject of combinatorial integral geometry received support from mathematicians K. Krickeberg and D. G. Kendall at the 1976 Sevan Symposium (Armenia) which was sponsored by Royal Society of London and The London Mathematical Society. In the framework of the later theory he solved a number of classical problems in particular the solution to the Buffon Sylvester problem as well as Hilbert's fourth problem in 1976. He is a holder of the Rollo Davidson Prize of Cambridge University of 1982. Rouben's interest in Integral Geometry was inherited from his father. Nobel prize winner Allan McLeod Cormack Laureate for Tomography wrote: "Ambartsumian gave the first numerical inversion of the Radon transform and it gives the lie to the often made statement that computed tomography would have been impossible without computers". Victor Hambardzumyan, in his book "A Life in Astrophysics", wrote about the work of Rouben V. Ambartzumian, "More recently, it came to my knowledge that the invariance principle or invariant embedding was applied in a purely mathematical field of integral geometry where it gave birth to a novel, combinatorial branch." See R. V. Ambartzumian, «Combinatorial Integral Geometry», John Wiley, 1982.
Jesper Møller is a Danish mathematician.
| International | |
|---|---|
| National | |
| Academics | |
| People | |
| Other | |
