|
Alexander Novikov (mathematician)
Alexander Novikov is a professor Emeritus at the Department of Mathematical Sciences, University of Technology Sydney. Prior to this current appointment in 1999 he was Leading Research Fellow at the Steklov Mathematical Institute (Moscow, since 1970) and Senior Lecture at the University of Newcastle ( Australia, from 1996 to 1999). Alexander was born in the Soviet Union, and currently lives in Australia. His research interest includes stochastic processes, statistics of random processes, sequential analysis, random fields, and mathematical finance. He is the author of Novikov's condition. He received a PhD in Mathematics in 1972 and his Doctor of Science degree in 1982, both from the Steklov Mathematical Institute, with his thesis supervised by Albert Shiryaev Albert Nikolayevich Shiryaev (russian: Альбе́рт Никола́евич Ширя́ев; born October 12, 1934) is a Soviet and Russian mathematician. He is known for his work in probability theory, statistics a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emeritus
''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title the rank of the last office held". In some cases, the term is conferred automatically upon all persons who retire at a given rank, but in others, it remains a mark of distinguished service awarded selectively on retirement. It is also used when a person of distinction in a profession retires or hands over the position, enabling their former rank to be retained in their title, e.g., "professor emeritus". The term ''emeritus'' does not necessarily signify that a person has relinquished all the duties of their former position, and they may continue to exercise some of them. In the description of deceased professors emeritus listed at U.S. universities, the title ''emeritus'' is replaced by indicating the years of their appointmentsThe Protoc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Field
In physics and mathematics, a random field is a random function over an arbitrary domain (usually a multi-dimensional space such as \mathbb^n). That is, it is a function f(x) that takes on a random value at each point x \in \mathbb^n(or some other domain). It is also sometimes thought of as a synonym for a stochastic process with some restriction on its index set. That is, by modern definitions, a random field is a generalization of a stochastic process where the underlying parameter need no longer be real or integer valued "time" but can instead take values that are multidimensional vectors or points on some manifold. Formal definition Given a probability space (\Omega, \mathcal, P), an ''X''-valued random field is a collection of ''X''-valued random variables indexed by elements in a topological space ''T''. That is, a random field ''F'' is a collection : \ where each F_t is an ''X''-valued random variable. Examples In its discrete version, a random field is a list of r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Living People
Related categories * :Year of birth missing (living people) / :Year of birth unknown * :Date of birth missing (living people) / :Date of birth unknown * :Place of birth missing (living people) / :Place of birth unknown * :Year of death missing / :Year of death unknown * :Date of death missing / :Date of death unknown * :Place of death missing / :Place of death unknown * :Missing middle or first names See also * :Dead people * :Template:L, which generates this category or death years, and birth year and sort keys. : {{DEFAULTSORT:Living people 21st-century people People by status ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Albert Shiryaev
Albert Nikolayevich Shiryaev (russian: Альбе́рт Никола́евич Ширя́ев; born October 12, 1934) is a Soviet and Russian mathematician. He is known for his work in probability theory, statistics and financial mathematics. Career He graduated from Moscow State University in 1957. From that time until now he has been working in Steklov Mathematical Institute. He earned his candidate degree in 1961 (Andrey Kolmogorov was his advisor) and a doctoral degree in 1967 for his work "On statistical sequential analysis". He is a professor of the department of mechanics and mathematics of Moscow State University, since 1971. Shiryaev holds a 20% permanent professorial position at the School of Mathematics, University of Manchester. He has supervised more than 50 doctoral dissertations and is the author or coauthor of more than 250 publications. In 1970 he was an Invited Speaker with talk ''Sur les equations stochastiques aux dérivées partielles'' at the Internati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Of Science
Doctor of Science ( la, links=no, Scientiae Doctor), usually abbreviated Sc.D., D.Sc., S.D., or D.S., is an academic research degree awarded in a number of countries throughout the world. In some countries, "Doctor of Science" is the degree used for the standard doctorate in the sciences; elsewhere the Sc.D. is a " higher doctorate" awarded in recognition of a substantial and sustained contribution to scientific knowledge beyond that required for a Doctor of Philosophy (PhD). Africa Algeria and Morocco In Algeria, Morocco, Libya and Tunisia, all universities accredited by the state award a "Doctorate" in all fields of science and humanities, equivalent to a PhD in the United Kingdom or United States. Some universities in these four Arab countries award a "Doctorate of the State" in some fields of study and science. A "Doctorate of the State" is slightly higher in esteem than a regular doctorate, and is awarded after performing additional in-depth post-doctorate research or ac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doctor Of Philosophy
A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is an earned research degree, those studying for a PhD are required to produce original research that expands the boundaries of knowledge, normally in the form of a dissertation, and defend their work before a panel of other experts in the field. The completion of a PhD is often a requirement for employment as a university professor, researcher, or scientist in many fields. Individuals who have earned a Doctor of Philosophy degree may, in many jurisdictions, use the title '' Doctor'' (often abbreviated "Dr" or "Dr.") with their name, although the proper etiquette associated with this usage may also be subject to the professional ethics of their own scholarly field, culture, or society. Those who teach at universities or work in academic, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Novikov's Condition
In probability theory, Novikov's condition is the sufficient condition for a stochastic process which takes the form of the Radon–Nikodym derivative in Girsanov's theorem to be a martingale. If satisfied together with other conditions, Girsanov's theorem may be applied to a Brownian motion stochastic process to change from the original measure to the new measure defined by the Radon–Nikodym derivative. This condition was suggested and proved by Alexander Novikov. There are other results which may be used to show that the Radon–Nikodym derivative is a martingale, such as the more general criterion Kazamaki's condition, however Novikov's condition is the most well-known result. Assume that (X_t)_ is a real valued adapted process on the probability space \left (\Omega, (\mathcal_t), \mathbb\right) and (W_t)_ is an adapted Brownian motion: If the condition : \mathbb\left ^ \right\infty is fulfilled then the process : \ \mathcal\left( \int_0^t X_s \; dW_s \r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Finance
Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets. In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering. The latter focuses on applications and modeling, often by help of stochastic asset models, while the former focuses, in addition to analysis, on building tools of implementation for the models. Also related is quantitative investing, which relies on statistical and numerical models (and lately machine learning) as opposed to traditional fundamental analysis when managing portfolios. French mathematician Louis Bachelier's doctoral thesis, defended in 1900, is considered the first scholarly work on mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sequential Analysis
In statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data are evaluated as they are collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results are observed. Thus a conclusion may sometimes be reached at a much earlier stage than would be possible with more classical hypothesis testing or estimation, at consequently lower financial and/or human cost. History The method of sequential analysis is first attributed to Abraham Wald with Jacob Wolfowitz, W. Allen Wallis, and Milton Friedman while at Columbia University's Statistical Research Group as a tool for more efficient industrial quality control during World War II. Its value to the war effort was immediately recognised, and led to its receiving a "restricted" classification. At the same time, George Barnard led a group working on optimal stopping in Great Britai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Technology Sydney
The University of Technology Sydney (UTS) is a public research university located in Sydney, New South Wales, Australia. Although its origins are said to trace back to the 1830s, the university was founded in its current form in 1988. As of 2021, UTS enrols 45,221 students through its 9 faculties and schools. The university is regarded as one of the world's leading young universities (under 50 years old), ranked 1st in Australia and 11th in the world by the 2021 QS World University Rankings Young Universities. UTS is a founding member of the Australian Technology Network, and is a member of Universities Australia and the Worldwide Universities Network. History The University of Technology Sydney originates from the Sydney Mechanics' School of Arts (the oldest continuously running Mechanics' Institute in Australia), which was established in 1833. In the 1870s, the School formed the Workingman's College, which was later taken over by the NSW government to form, in 1882, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Process
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. 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, cryptography and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of such stochastic processes include the Wiener process or Brownian motion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
