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pro vyhledávání: '"Hocquet, Antoine"'
A summary of recent contributions in the field of rough partial differential equations is given. For that purpose we rely on the formalism of ``unbounded rough driver''. We present applications to concrete models including Landau-Lifshitz-Gilbert, Na
Externí odkaz:
http://arxiv.org/abs/2501.01186
Autor:
Hocquet, Antoine, Neamţu, Alexandra
We investigate the abstract Cauchy problem for a quasilinear parabolic equation in a Banach space of the form \( du_t -L_t(u_t)u_t dt = N_t(u_t)dt + F(u_t)\cdot d\mathbf X_t \), where \( \mathbf X\) is a \( \gamma\)-H\"older rough path for \( \gamma\
Externí odkaz:
http://arxiv.org/abs/2207.04787
Autor:
Hocquet, Antoine, Vogler, Alexander
We introduce a variant of the multiplicative Sewing Lemma in [Gerasimovi\v{c}s, Hocquet, Nilssen; J. Funct. Anal. 281 (2021)] which yields arbitrary high order weak approximations to stochastic differential equations, extending the cubature approxima
Externí odkaz:
http://arxiv.org/abs/2206.10297
We establish a simultaneous generalization of It\^o's theory of stochastic and Lyons' theory of rough differential equations. The interest in such a unification comes from a variety of applications, including pathwise stochastic filtering, - control
Externí odkaz:
http://arxiv.org/abs/2106.10340
Autor:
Gussetti, Emanuela, Hocquet, Antoine
Using a rough path formulation, we investigate existence, uniqueness and regularity for the stochastic Landau-Lifshitz-Gilbert equation with Stratonovich noise on the one dimensional torus. As a main result we show the continuity of the so-called It\
Externí odkaz:
http://arxiv.org/abs/2103.00926
Autor:
Hocquet, Antoine, Vogler, Alexander
We are interested in the optimal control problem associated with certain quadratic cost functionals depending on the solution $X=X^\alpha$ of the stochastic mean-field type evolution equation in $\mathbb R^d$ $dX_t=b(t,X_t,\mathcal L(X_t),\alpha_t)dt
Externí odkaz:
http://arxiv.org/abs/2007.01321
Autor:
Hocquet, Antoine, Vogler, Alexander
Publikováno v:
In Stochastic Processes and their Applications November 2023 165:183-217
Autor:
Gussetti, Emanuela, Hocquet, Antoine
Publikováno v:
In Journal of Functional Analysis 1 November 2023 285(9)
We investigate existence, uniqueness and regularity for local solutions of rough parabolic equations with subcritical noise of the form $du_t- L_tu_tdt= N(u_t)dt + \sum_{i = 1}^dF_i(u_t)d\mathbf X^i_t$ where $(L_t)_{t\in[0,T]}$ is a time-dependent fa
Externí odkaz:
http://arxiv.org/abs/1907.13398
We investigate existence and uniqueness for the stochastic liquid crystal flow driven by colored noise on the two-dimensional torus. After giving a natural uniqueness criterion, we prove local solvability in $L^p$-based spaces, for every $p>2.$ Thank
Externí odkaz:
http://arxiv.org/abs/1902.05921