@prefix dcat: <http://www.w3.org/ns/dcat#> .
@prefix dct: <http://purl.org/dc/terms/> .
@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix vcard: <http://www.w3.org/2006/vcard/ns#> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

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              This paper considers the class of stochastic processes $X$ which are Volterra convolutions of a martingale $M$. When $M$ is Brownian motion, $X$ is Gaussian, and the class includes fractional Brownian motion and other Gaussian processes with or without homogeneous increments. Let $m$ be an odd integer. Under some technical conditions on the quadratic variation of $M$, it is shown that the $m$-power variation exists and is zero when a quantity $\\delta^{2}(r) $ related to the variance of an increment of $M$ over a small interval of length $r$ satisfies $\\delta(r) = o(r^{1/(2m)}) $. In the case of a Gaussian process with homogeneous increments, $\\delta$ is $X$'s canonical metric and the condition on $\\delta$ is proved to be necessary, and the zero variation result is extended to non-integer symmetric powers. In the non-homogeneous Gaussian case, when $m=3$, the symmetric (generalized Stratonovich) integral is defined, proved to exist, and its Itô's formula is proved to hold for all functions of class $C^{6}$.
            """ ;
    dct:identifier "inria-00438532" ;
    dct:issued "2026-05-16T19:39:45.010345"^^xsd:dateTime ;
    dct:language "en" ;
    dct:modified "2026-05-16T19:39:45.010352"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Gaussian and non-Gaussian processes of zero power variation" ;
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    dct:issued "2026-05-16T19:39:45.026742"^^xsd:dateTime ;
    dct:modified "2026-05-16T19:39:44.958162"^^xsd:dateTime ;
    dct:title "Gaussian and non-Gaussian processes of zero power variation" ;
    dcat:accessURL <https://inria.hal.science/inria-00438532> .

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