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pro vyhledávání: '"Bailleul, Ismael"'
We argue that the spectrally cut-off Gaussian free field $\Phi_\Lambda$ on a compact Riemannian manifold or on $\mathbb{R}^n$ cannot satisfy the spatial Markov property. Moreover, when the manifold is reflection positive, we show that $\Phi_\Lambda$
Externí odkaz:
http://arxiv.org/abs/2312.15511
We introduce Wilson-It\^o diffusions, a class of random fields on $\mathbb{R}^d$ that change continuously along a scale parameter via a Markovian dynamics with local coefficients. Described via forward-backward stochastic differential equations, thei
Externí odkaz:
http://arxiv.org/abs/2307.11580
Autor:
Bailleul, Ismael, Bruned, Yvain
Extended decorations on naturally decorated trees were introduced in the work of Bruned, Hairer and Zambotti on algebraic renormalization of regularity structures to provide a convenient framework for the renormalization of systems of singular stocha
Externí odkaz:
http://arxiv.org/abs/2101.11949
Publikováno v:
ESAIM: Proceedings and Surveys, Vol 74, Pp 169-184 (2023)
After a brief survey on rough paths theory, from the seminal paper of T. Lyons to its recent developments, this proceeding provides details on C. Bellingeri, Y. Bruned and A. Fermanian’s talks during the Journées MAS 2020: a new formulation and a
Externí odkaz:
https://doaj.org/article/8662d5fcb7d04991bd7d45c889f7bbf4
Autor:
Bailleul, Ismael, Norris, James
Publikováno v:
Analysis & PDE 15 (2022) 63-84
For incomplete sub-Riemannian manifolds, and for an associated second-order hypoelliptic operator, which need not be symmetric, we identify two alternative conditions for the validity of Gaussian-type upper bounds on heat kernels and transition proba
Externí odkaz:
http://arxiv.org/abs/1810.06328
We analyze common lifts of stochastic processes to rough paths/rough drivers-valued processes and give sufficient conditions for the cocycle property to hold for these lifts. We show that random rough differential equations driven by such lifts induc
Externí odkaz:
http://arxiv.org/abs/1612.01955
We present in this note a local in time well-posedness result for the singular $2$-dimensional quasilinear generalized parabolic Anderson model equation $$ \partial_t u - a(u)\Delta u = g(u)\xi $$ The key idea of our approach is a simple transformati
Externí odkaz:
http://arxiv.org/abs/1610.06726
We consider small-time asymptotics for diffusion processes conditioned by their initial and final positions, under the assumption that the diffusivity has a sub-Riemannian structure, not necessarily of constant rank. We show that, if the endpoints ar
Externí odkaz:
http://arxiv.org/abs/1505.03464
We consider in this work a one parameter family of hypoelliptic diffusion processes on the unit tangent bundle $T^1 \mathcal M$ of a Riemannian manifold $(\mathcal M,g)$, collectively called kinetic Brownian motions, that are random perturbations of
Externí odkaz:
http://arxiv.org/abs/1501.03679
Autor:
Bailleul, Ismael
These are lecture notes for a Master 2 course on rough differential equations driven by weak geometric Holder p-rough paths, for any p>2. They provide a short, self-contained and pedagogical account of the theory, with an emphasis on flows. The theor
Externí odkaz:
http://arxiv.org/abs/1404.0890