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Excursion Probability
In probability theory, an excursion probability is the probability that a stochastic process surpasses a given value in a fixed time period. It is the probability :\mathbb P \left\. Numerous approximation methods for the situation where ''u'' is large and f(''t'') is a Gaussian process have been proposed such as Rice's formula In probability theory, Rice's formula counts the average number of times an ergodic stationary process ''X''(''t'') per unit time crosses a fixed level ''u''. Adler and Taylor describe the result as "one of the most important results in the applic .... First-excursion probabilities can be used to describe deflection to a critical point experienced by structures during "random loadings, such as earthquakes, strong gusts, hurricanes, etc." References Stochastic processes {{probability-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion). Although it is not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability ... [...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 process, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Process
In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random variables, and as such, it is a distribution over functions with a continuous domain, e.g. time or space. The concept of Gaussian processes is named after Carl Friedrich Gauss because it is based on the notion of the Gaussian distribution (normal distribution). Gaussian processes can be seen as an infinite-dimensional generalization of multivariate normal distributions. Gaussian processes are useful in statistical modelling, benefiting from properties inherited from the normal distribution. For example, if a random process is modelled as a Gaussian process, the distribution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rice's Formula
In probability theory, Rice's formula counts the average number of times an ergodic stationary process ''X''(''t'') per unit time crosses a fixed level ''u''. Adler and Taylor describe the result as "one of the most important results in the applications of smooth stochastic processes." The formula is often used in engineering. History The formula was published by Stephen O. Rice in 1944, having previously been discussed in his 1936 note entitled "Singing Transmission Lines." Formula Write ''D''''u'' for the number of times the ergodic stationary stochastic process ''x''(''t'') takes the value ''u'' in a unit of time (i.e. ''t'' ∈ ,1. Then Rice's formula states that ::\mathbb E(D_u) = \int_^\infty , x', p(u,x') \, \mathrmx' where ''p''(''x'',''x''') is the joint probability density of the ''x''(''t'') and its mean-square derivative ''x(''t''). If the process ''x''(''t'') is a Gaussian process and ''u'' = 0 then the formula simplifies significantly to give ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Annals Of Applied Probability
'' The Annals of Applied Probability'' is a leading peer-reviewed mathematics journal published by the Institute of Mathematical Statistics, which is the main international society for researchers in probability and statistics. The journal was established in 1991 by founding editor J. Michael Steele and is indexed by ''Mathematical Reviews'' and Zentralblatt MATH. Its 2009 MCQ was 1.02. Its impact factor (measured by JCR/ISI-Thomson) evolved from 1.454 in 2014 to 1.786 in 2017. The journal CiteScore is 3.2 and its SCImago Journal Rank The SCImago Journal Rank (SJR) indicator is a measure of the prestige of scholarly journals that accounts for both the number of citations received by a journal and the prestige of the journals where the citations come from. Rationale Citati ... is 1.878, both from 2020. It is currently ranked 9th in the field of Probability & Statistics with Applications according to Google Scholar. References External links * Probability journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Sound And Vibration
The ''Journal of Sound and Vibration'' is a scientific journal in the field of acoustics. It is published by Elsevier. The journal is devoted to the prompt publication of original papers, both theoretical and experimental, that provide new information on any aspect of sound or vibration. According to the ''Journal Citation Reports'', the journal has a 2021 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... of 4.761. External links Journal Homepage References Elsevier academic journals Acoustics journals Biweekly journals Publications established in 1964 {{acoustics-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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