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...="KallebergFoundations286" /> As a result, some authors immediately define Lévy process as being càdlàg and having independent increments.<ref name="Kalleb ...s on Lévy processes and Stochastic calculus, Braunschweig; Lecture 2: Lévy processes|url=http://www.applebaum.staff.shef.ac.uk/Brauns2notes.pdf|author=Applebaum ...

...ble process''' is a type of [[stochastic process]]. It includes stochastic processes whose associated [[probability distribution]]s are [[stable distributions]] Examples of stable processes include the [[Wiener process]], or [[Brownian motion]], whose associated pr ...

...e|year=1983|title=The isoperimetric inequality for isotropic unimodal Lévy processes|journal=Z. Wahrsch. Verw. Gebiete|volume=63 |issue=4|pages=487–499}}</ref> == Isotropic and unimodal stochastic processes == ...

...ochastic processes have stationary increments either by definition (e.g. [[Lévy process]]es) or by construction (e.g. [[random walk]]s) ...isson process]]es have stationary increments. Other families of stochastic processes such as [[random walk]]s have stationary increments by construction. ...

...of Reflected Solutions of Stochastic Equations Driven by Symmetric Stable Processes|author=Engelbert, H.J., Kurenok, V.P. & Zalinescu, A.|page=[https://archive ...es: Theory and Methods|editor=Shanbhag, D.N.|chapter=Some elements on Lévy processes|author=Bertoin, J.|page=122|year=2001|publisher=Gulf Professional Publishin ...

...of these is attributed to {{harvs|txt|first=Paul|last=Lévy|authorlink=Paul Lévy (mathematician)|year=1939}}. ...y|Scale invariance]] ensures that the results can be generalised to Wiener processes run for ''t''&nbsp;&isin;[0,&infin;). ...

...f name="KallebergFoundations290" /> Subordinators are a special class of [[Lévy process]] that play an important role in the theory of [[local time (mathem ...s on Lévy processes and Stochastic calculus, Braunschweig; Lecture 2: Lévy processes|url=http://www.applebaum.staff.shef.ac.uk/Brauns2notes.pdf|author=Applebaum ...

...467 }}</ref> and in 1950<ref name="Levy">{{cite journal|first=Paul M.|last=Lévy|title=Wiener's random function, and other Laplacian random functions|journa ==Lévy's stochastic area== ...

...exist a slightly different version due to [[Paul Lévy (mathematician)|Paul Lévy]]. === Lévy's definition of the multiparametric Brownian motion === ...

...the [[geometric Brownian motion]]{{sfn|Peres|Sousi|2016}} or stable [[Lévy processes]]{{sfn|Kern|Pleschberger|2024}} plus [[Borel measurable]] drift function <m For an isotropic <math>\alpha</math>-stable Lévy process <math>X</math> for <math>\alpha \in (0,2]</math> plus some measurab ...

...tegral]], where the [[integral|integration]] is done with respect to a ''[[Lévy basis]]'', plus a smooth term given by an ordinary [[Lebesgue integration|L ...tp://data.imf.au.dk/publications/thiele/2005/imf-thiele-2005-14.pdf "Ambit processes; with applications to turbulence and tumour growth"], ''Research report, Th ...

==Extension to stable processes== ...ential equations driven by stable Lévy motion|year=1997|journal=Stochastic Processes and Their Applications|volume=68|pages=209–228|doi=10.1214/aop/1023481008|u ...

...ath>p</math>-th moments for all <math>p>\alpha</math>, the tempered stable processes have been proposed for overcoming this limitation of the stable distributio ...] <math>\nu</math> on <math>\mathbb{R}</math> is called a [[Levy measure|''Lévy measure'']] if <math>\nu({0})=0</math> and ...

...th stationary increments). An example of an additive process that is not a Lévy process is a [[Brownian motion]] with a time-dependent drift.{{sfn|Tankov|C The additive process was introduced by [[Paul Lévy (mathematician)|Paul Lévy]] in 1937.{{sfn|Tankov|Cont|2003|p=468}} ...

...''a''.<ref name=Jacobs>{{cite book|last=Jacobs|first=Kurt|title=Stochastic Processes for Physicists|year=2010|publisher=Cambridge University Press|isbn=97811394 Assuming <math> W(0) = 0 </math> , due to the continuity of Wiener processes, each path (one sampled realization) of Wiener process on <math> (0,t) </ma ...

...ariance-Gamma-process.png|thumb|right|Three sample paths of variance gamma processes (in resp. red, green, black)]] ...finite [[moment (mathematics)|moments]], distinguishing it from many Lévy processes. There is no [[diffusion]] component in the VG process and it is thus a [[ ...

...oi=10.4153/CJM-1958-026-0|title=Central Limit Theorems for Interchangeable Processes|year=1958|last1=Blum|first1=J. R.|last2=Chernoff|first2=H.|last3=Rosenblatt ===Lévy process=== ...

| title =Cuckoo search via Lévy flights ...Deb discovered that the random-walk style search is better performed by [[Lévy flight]]s rather than simple [[random walk]]. ...

...ner process]] (or [[Brownian motion]]). Realisations of Brownian excursion processes are essentially just realizations of a Wiener process selected to satisfy c ...f a Brownian motion process ''W'' (due to [[Paul Lévy (mathematician)|Paul Lévy]] and noted by [[Kiyosi Itô]] and [[Henry McKean|Henry P. McKean, Jr.]]<ref ...

...rvtxt|Barendregt|1977}} and named after a theorem of [[Corrado Böhm]]}} '''Lévy-Longo trees''',<ref>{{cite book |last1=Levy |first1=Jean-Jacques |title=λ-C === Lévy-Longo trees === ...