deterministic) Lévy processes have discontinuous paths. All Lévy processes are additive processes. A Lévy process is a stochastic process X = { X t : t...

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...

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...

Bertoin (1998). Lévy Processes. Cambridge University Press. p. viii. ISBN 978-0-521-64632-1. Applebaum, David (2004). "Lévy processes: From probability...

These processes exhaust continuous Lévy processes, which means that they are the only continuous Lévy processes, as a consequence of the Lévy–Khintchine...

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...

system in a given state Lévy process, a stochastic process with independent, stationary increments Poisson process, a point process consisting of randomly...

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...

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"...

In probability theory and statistics, the Lévy distribution, named after Paul Lévy, is a continuous probability distribution for a non-negative random...

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...

statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in...

resulting compound Poisson process is an example of a Lévy process provided that it is formed from a homogeneous Point process N {\displaystyle \textstyle...

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...

stationary processes, also called time-homogeneous. Karhunen–Loève theorem Lévy process Local time (mathematics) Loop-erased random walk Markov processes are...

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...

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...

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...

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...

(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...

A jump process is a type of stochastic process that has discrete movements, called jumps, with random arrival times, rather than continuous movement,...

wavelet transform and Fourier transform may also be helpful. Lévy process Stationary ergodic process Wiener–Khinchin theorem Ergodicity Statistical regularity...

process was introduced by Paul Lévy in 1940, and in 1950 he computed the characteristic function and conditional characteristic function. The process...

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...

families of stochastic processes such as the Lévy processes. Being special Lévy processes, both the Wiener process and the Poisson processes have stationary...

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...

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...

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...

the stochastic processes that by definition possess independent increments are the Wiener process, all Lévy processes, all additive process and the Poisson...

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...