TY  - JOUR
A1  - Mazzonetto, Sara
T1  - On an approximation of 2-D stochastic Navier-Stokes equations
JF  - Lectures in pure and applied mathematics
KW  - random point processes
KW  - statistical mechanics
KW  - stochastic analysis
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-472053
SN  - 978-3-86956-485-2
SN  - 2199-4951
SN  - 2199-496X
IS  - 6
SP  - 87
EP  - 96
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Mazzonetto, Sara
A1  - Salimova, Diyora
T1  - Existence, uniqueness, and numerical approximations for stochastic burgers equations
JF  - Stochastic analysis and applications
N2  - In this article, we propose an all-in-one statement which includes existence, uniqueness, regularity, and numerical approximations of mild solutions for a class of stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities. The proof of this result exploits the properties of an existing fully explicit space-time discrete approximation scheme, in particular the fact that it satisfies suitable a priori estimates. We also obtain almost sure and strong convergence of the approximation scheme to the mild solutions of the considered SPDEs. We conclude by applying the main result of the article to the stochastic Burgers equations with additive space-time white noise.
KW  - Stochastic Burgers equations
KW  - SPDEs
KW  - mild solution
KW  - existence
KW  - numerical
KW  - approximation
Y1  - 2020
U6  - https://doi.org/10.1080/07362994.2019.1709503
SN  - 0736-2994
SN  - 1532-9356
VL  - 38
IS  - 4
SP  - 623
EP  - 646
PB  - Taylor & Francis Group
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Dereudre, David
A1  - Mazzonetto, Sara
A1  - Roelly, Sylvie
T1  - Exact simulation of Brownian diffusions with drift admitting jumps
JF  - SIAM journal on scientific computing
N2  - In this paper, using an algorithm based on the retrospective rejection sampling scheme introduced in [A. Beskos, O. Papaspiliopoulos, and G. O. Roberts,Methodol. Comput. Appl. Probab., 10 (2008), pp. 85-104] and [P. Etore and M. Martinez, ESAIM Probab.Stat., 18 (2014), pp. 686-702], we propose an exact simulation of a Brownian di ff usion whose drift admits several jumps. We treat explicitly and extensively the case of two jumps, providing numerical simulations. Our main contribution is to manage the technical di ffi culty due to the presence of t w o jumps thanks to a new explicit expression of the transition density of the skew Brownian motion with two semipermeable barriers and a constant drift.
KW  - exact simulation methods
KW  - skew Brownian motion
KW  - skew diffusions
KW  - Brownian motion with discontinuous drift
Y1  - 2017
U6  - https://doi.org/10.1137/16M107699X
SN  - 1064-8275
SN  - 1095-7197
VL  - 39
IS  - 3
SP  - A711
EP  - A740
PB  - Society for Industrial and Applied Mathematics
CY  - Philadelphia
ER  -