12 citations · 16 across the 10 of their papers we have counts for
16 papers
McKean-Vlasov equations with rough common noise
Peter K. Friz, Antoine Hocquet, Khoa Lê
We show well-posedness for McKean--Vlasov equations with rough common noise and progressively measurable coefficients. Our results are valid under natural regularity assumptions on…
Unbounded rough drivers, rough PDEs and applications
Antoine Hocquet, Martina Hofmanova, Torstein Nilssen
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…
Quasilinear rough evolution equations
Antoine Hocquet, Alexandra Neamţu
We investigate the abstract Cauchy problem for a quasilinear parabolic equation in a Banach space of the form \( du_t -L_t(u_t)u_t dt = N_t(u_t)dt + F(u_t)\cdot d\mathbf X_t \), wh…
An application of the multiplicative Sewing Lemma to the high order weak approximation of stochastic differential equations
Antoine Hocquet, Alexander Vogler
We introduce a variant of the multiplicative Sewing Lemma in [Gerasimovičs, Hocquet, Nilssen; J. Funct. Anal. 281 (2021)] which yields arbitrary high order weak approximations to s…
Rough stochastic differential equations
Peter K. Friz, Antoine Hocquet, Khoa Lê
We establish a simultaneous generalization of Itô's theory of stochastic and Lyons' theory of rough differential equations. The interest in such a unification comes from a variety…
A pathwise stochastic Landau-Lifshitz-Gilbert equation with application to large deviations
Emanuela Gussetti, Antoine Hocquet
Using a rough path formulation, we investigate existence, uniqueness and regularity for the stochastic Landau-Lifshitz-Gilbert equation with Stratonovich noise on the one dimension…
Optimal control of mean field equations with monotone coefficients and applications in neuroscience
Antoine Hocquet, Alexander Vogler
We are interested in the optimal control problem associated with certain quadratic cost functionals depending on the solution of the stochastic mean-field type evolution eq…
Non-autonomous rough semilinear PDEs and the multiplicative Sewing Lemma
Andris Gerasimovics, Antoine Hocquet, Torstein Nilssen
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_…
Existence, uniqueness and regularity for the stochastic Ericksen-Leslie equation
Anne De Bouard, Antoine Hocquet, Andreas Prohl
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…
Quasilinear rough partial differential equations with transport noise
Antoine Hocquet
We investigate the Cauchy problem for a quasilinear equation with transport rough input of the form $\mathrm{d} u-\partial_i(a^{ij}(u)\partial_j u)\mathrm{d} t =\mathrm{d} \mathbf{…
An Itô Formula for rough partial differential equations and some applications
Antoine Hocquet, Torstein Nilssen
We investigate existence, uniqueness and regularity for solutions of rough parabolic equations of the form on $[0,T]…
Generalized Burgers equation with rough transport noise
Antoine Hocquet, Torstein Nilssen, Wilhelm Stannat
We introduce a new technique for studying well posedness and energy estimates for evolution equations with a rough transport term. The technique is based on finding suitable space-…
An energy method for rough partial differential equations
Antoine Hocquet, Martina Hofmanová
We present a well-posedness and stability result for a class of nondegenerate linear parabolic equations driven by rough paths. More precisely, we introduce a notion of weak soluti…
Struwe-like solutions for the Stochastic Harmonic Map Flow
Antoine Hocquet
We give a new result on the well-posedness of the two-dimensional Stochastic Harmonic Map flow, whose study is motivated by the Landau-Lifshitz-Gilbert model for thermal fluctuatio…
Finite-time singularity of the stochastic harmonic map flow
Antoine Hocquet
We investigate the influence of an infinite dimensional Gaussian noise on the bubbling phenomenon for the stochastic harmonic map flow , fr…
A semi-discrete scheme for the stochastic Landau-Lifshitz equation
François Alouges, Anne De Bouard, Antoine Hocquet
We propose a new convergent time semi-discrete scheme for the stochastic Landau-Lifshitz-Gilbert equation. The scheme is only linearly implicit and does not require the resolution…