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pro vyhledávání: '"Christian Olivera"'
We prove the existence and the Besov regularity of the density of the solution to a general parabolic SPDE which includes the stochastic Burgers equation on an unbounded domain. We use an elementary approach based on the fractional integration by par
Externí odkaz:
http://arxiv.org/abs/2103.03812
Autor:
Benedetta Ferrario, Christian Olivera
Publikováno v:
AIMS Mathematics, Vol 3, Iss 4, Pp 539-553 (2018)
We study the Navier-Stokes equations on a smooth bounded domain $D\subset \mathbb R^d$ ($d=2$ or 3), under the effect of an additive fractional Brownian noise. We show local existence and uniqueness of a mild $L^p$-solution for $p>d$.
Externí odkaz:
https://doaj.org/article/79c8df45e7734f838d9bde374285f305
Autor:
Christian Olivera
Publikováno v:
Mathematical Research Letters. 28:563-573
This paper is based on a formulation of the Navier-Stokes equations developed by Iyer and Constantin \cite{Cont} , where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. Our contribution i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5e5e966d195a54c7adc30c40ba0236b9
https://doi.org/10.4310/mrl.2021.v28.n2.a8
https://doi.org/10.4310/mrl.2021.v28.n2.a8
Autor:
Christian Olivera, Wladimir Neves
Publikováno v:
Stochastics and Partial Differential Equations: Analysis and Computations. 9:674-701
This paper concerns the Dirichlet initial-boundary value problem for stochastic transport equations with non-regular coefficients. First, the existence and uniqueness of the strong stochastic traces is proved. The existence of weak solutions relies o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::05ce5bce960042fc23f6df3286e94834
https://doi.org/10.1007/s40072-020-00180-9
https://doi.org/10.1007/s40072-020-00180-9
Autor:
Christian Olivera, Evelina Shamarova
Publikováno v:
Mathematische Nachrichten. 293:1554-1564
We obtain upper and lower Gaussian density estimates for the laws of each component of the solution to a one‐dimensional fully coupled forward‐backward SDE. Our approach relies on the link between FBSDEs and quasilinear parabolic PDEs, and is ful
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dff7c6d9d3733af6b837a095f3d92cd7
https://doi.org/10.1002/mana.201800381
https://doi.org/10.1002/mana.201800381
Autor:
Ciprian A. Tudor, Christian Olivera
Publikováno v:
Comptes Rendus Mathematique. 357:636-645
By using a simple method based on the fractional integration by parts, we prove the existence and the Besov regularity of the density for solutions to stochastic differential equations driven by an additive Gaussian Volterra process. We assume weak r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::33428ac5aad21557574153c46dbf7854
https://doi.org/10.1016/j.crma.2019.06.012
https://doi.org/10.1016/j.crma.2019.06.012
Autor:
Wladimir Neves, Christian Olivera
We study in this article the existence and uniqueness of solutions to a class of stochastic transport equations with irregular coefficients and unbounded divergence. In the first result we assume the drift is $L^{2}([0,T] \times \R^{d})\cap L^{\infty
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d3c0adf8f8483fdde490589a8fae4519
Publikováno v:
SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2020, 52 (6), ⟨10.1137/20M1328993⟩
SIAM Journal on Mathematical Analysis, 2020, 52 (6), ⟨10.1137/20M1328993⟩
SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2020, 52 (6), ⟨10.1137/20M1328993⟩
SIAM Journal on Mathematical Analysis, 2020, 52 (6), ⟨10.1137/20M1328993⟩
We consider an interacting particle system modeled as a system of N stochastic differential equations driven by Brownian motions. We prove that the (mollified) empirical process converges, uniformly in time and space variables, to the solution of the
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cc54ccbd3eea595e0502ad6c40a23643
https://hal.inria.fr/hal-02529632/document
https://hal.inria.fr/hal-02529632/document
Autor:
Hugo De la Cruz, Christian Olivera
Publikováno v:
Proceeding Series of the Brazilian Society of Computational and Applied Mathematics.
We consider d−dimensional PDEs of convention-diffusion type with at most Holder continuous coefficients. We construct an stochastic numerical method for the Monte Carlo integration of this kind of equations. The proposed approach is based on the pr
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b23d815ee4dce54791ca7eaf77b414e1
https://doi.org/10.5540/03.2020.007.01.0342
https://doi.org/10.5540/03.2020.007.01.0342
Autor:
Christian Olivera, Benedetta Ferrario
Publikováno v:
Annali di Matematica Pura ed Applicata (1923 -). 198:1041-1067
We consider the Navier–Stokes equation on the 2D torus, with a stochastic forcing term which is a cylindrical fractional Wiener noise of Hurst parameter H. Following Albeverio and Ferrario (Ann Probab 32(2):1632–1649, 2004) and Da Prato and Debus
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::83993eaadfb4756099831ba967e5c349
https://doi.org/10.1007/s10231-018-0809-x
https://doi.org/10.1007/s10231-018-0809-x