deterministic) Lévy processes have discontinuous paths. All Lévy processes are additive processes. A Lévy process is a stochastic process X = { X t : t...
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functions. Lévy processes, Lévy flights, Lévy measures, Lévy's constant, the Lévy distribution, the Lévy area, the Lévy arcsine law, and the fractal Lévy C curve...
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Infinite divisibility (probability) (redirect from Infinitely divisible process)
probability distribution corresponds in a natural way to a Lévy process. A Lévy process is a stochastic process { Lt : t ≥ 0 } with stationary independent increments...
9 KB (1,056 words) - 20:03, 11 April 2024
Bertoin (1998). Lévy Processes. Cambridge University Press. p. viii. ISBN 978-0-521-64632-1. Applebaum, David (2004). "Lévy processes: From probability...
162 KB (17,919 words) - 13:01, 18 August 2024
These processes exhaust continuous Lévy processes, which means that they are the only continuous Lévy processes, as a consequence of the Lévy–Khintchine...
35 KB (5,899 words) - 19:42, 30 July 2024
of a Lévy process (a Lévy process is an additive process with stationary increments). An example of an additive process that is not a Lévy process is a...
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system in a given state Lévy process, a stochastic process with independent, stationary increments Poisson process, a point process consisting of randomly...
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interpreted as the Bernoulli process. One may generalize this to include continuous time Lévy processes, and many Lévy processes can be seen as limits of...
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term "Lévy flight" to also include cases where the random walk takes place on a discrete grid rather than on a continuous space. The term "Lévy flight"...
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In probability theory and statistics, the Lévy distribution, named after Paul Lévy, is a continuous probability distribution for a non-negative random...
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of a Lévy process (or semigroup) is a Fourier multiplier operator with symbol − ψ {\displaystyle -\psi } . Let L {\textstyle L} be a Lévy process with...
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statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in...
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resulting compound Poisson process is an example of a Lévy process provided that it is formed from a homogeneous Point process N {\displaystyle \textstyle...
118 KB (15,546 words) - 08:33, 6 August 2024
symmetric Cauchy process can be described by a Brownian motion or Wiener process subject to a Lévy subordinator. The Lévy subordinator is a process associated...
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stationary processes, also called time-homogeneous. Karhunen–Loève theorem Lévy process Local time (mathematics) Loop-erased random walk Markov processes are...
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Autoregressive model (redirect from Autoregressive process)
statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it can be used to describe...
35 KB (5,416 words) - 17:26, 7 July 2024
Lévy-driven Ornstein–Uhlenbeck process, in which the background driving process is a Lévy process instead of a Wiener process: d x t = − θ x t d t + σ d L...
30 KB (4,607 words) - 06:49, 22 July 2024
t {\displaystyle t} represents the time from 0. The process is a pure-jump increasing Lévy process with intensity measure ν ( x ) = γ x − 1 exp ( − λ...
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Subordinator (mathematics) (category Stochastic processes)
ISBN 978-3-319-41596-3. Applebaum, D. "Lectures on Lévy processes and Stochastic calculus, Braunschweig; Lecture 2: Lévy processes" (PDF). University of Sheffield. pp...
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(the Wiener process). The best known of these is attributed to Paul Lévy (1939). All three laws relate path properties of the Wiener process to the arcsine...
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A jump process is a type of stochastic process that has discrete movements, called jumps, with random arrival times, rather than continuous movement,...
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wavelet transform and Fourier transform may also be helpful. Lévy process Stationary ergodic process Wiener–Khinchin theorem Ergodicity Statistical regularity...
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process was introduced by Paul Lévy in 1940, and in 1950 he computed the characteristic function and conditional characteristic function. The process...
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stochastic processes is the Lévy–Itō decomposition: given a Lévy process X, it can be decomposed as a sum of three independent Lévy processes X = X ( 1...
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Stationary increments (category Stochastic processes)
families of stochastic processes such as the Lévy processes. Being special Lévy processes, both the Wiener process and the Poisson processes have stationary...
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Stable distribution (redirect from Lévy skew alpha-stable distribution)
distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the...
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the distribution of a Lévy process at one point in time belongs to one of these families, then the distribution of the Lévy process at all points in time...
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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...
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the stochastic processes that by definition possess independent increments are the Wiener process, all Lévy processes, all additive process and the Poisson...
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Gaussian random field (category Spatial processes)
functions of the variables. A one-dimensional GRF is also called a Gaussian process. An important special case of a GRF is the Gaussian free field. With regard...
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