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Backward Stochastic Differential Equations Associated to a Symmetric Markov Process
Springer Science and Business Media LLC - Tập 22 - Trang 17-60 - 2005
We consider a second order semi-elliptic differential operator L with measurable
coefficients, in divergence form, and the semilinear parabolic system of PDE’s
$$\begin{gathered} \left( {\partial _t + L} \right)u\left( {t,x} \right) +
f\left( {t,x,u,\nabla u\sigma } \right) = \forall 0 \leqslant t \leqslant T,
\hfill \\ u\left( {T,x} \right) = \Phi \left( x \right). \hfill \\
\end{gathered} $$ We ...
Random walks on finitely structured transfinite networks
Springer Science and Business Media LLC - - 1996
Quelques resultats d'entropie sur l'espace de Wiener
Springer Science and Business Media LLC - Tập 1 - Trang 167-176 - 1992
One studies three problems related to entropy phenomenon in the classical Wiener
space. In particular, the minoration of the Wiener measure for the set
{x∈X/ϕ(x)⩽ε} is given where ϕ is a Sobolev norm in the Wiener spaceX.
Two-Weight Inequalities for Multilinear Commutators in Product Spaces
Springer Science and Business Media LLC - Tập 59 - Trang 1745-1792 - 2022
This article is devoted to establishing two-weight estimates for commutators of
singular integrals. We combine multilinearity with product spaces. A new type of
two-weight extrapolation result is used to yield the quasi-Banach range of
estimates.
A property of nonlinear elliptic equations when the right-hand side is a measure
Springer Science and Business Media LLC - - 1994
Tangential Boundary Behaviour of Harmonic Functions on Trees
Springer Science and Business Media LLC - Tập 6 - Trang 269-287 - 1997
We study the behaviour of harmonic functions on a homogeneous tree from the
point of view of the tangential boundary covergence.
Harnack Inequalities for SDEs Driven by Cylindrical α-Stable Processes
Springer Science and Business Media LLC - Tập 42 - Trang 657-669 - 2014
By using the coupling argument, we establish the Harnack and log-Harnack
inequalites for stochastic differential equations with non-Lipschitz drifts and
driven by additive anisotropic subordinated Brownian motions (in particular,
cylindrical α-stable processes). Moreover, the gradient estimate is also derived
when the drift is Lipschitz continuous.
Comparaison des semi-groupes et des résolvantes d'ordre α associés à des opérateurs différentiels de type divergence
Springer Science and Business Media LLC - Tập 3 - Trang 15-45 - 1994
We prove that the densities of the semi-groups of order α, 0<α<1 associated with
differential operators of second order and of divergence type, and the density
of Riesz semi-groups of order α are comparables. We give a necessary and
sufficient condition such that the semi-group of order α and its resolvent
family and their perturbated with a nonnegative and regular Radon measure are
comparables. W...
Central Limit Theorems for Non-Symmetric Random Walks on Nilpotent Covering Graphs: Part II
Springer Science and Business Media LLC - Tập 55 - Trang 127-166 - 2020
In the present paper, as a continuation of our preceding paper (Ishiwata et al.
2018), we study another kind of central limit theorems (CLTs) for non-symmetric
random walks on nilpotent covering graphs from a view point of discrete
geometric analysis developed by Kotani and Sunada. We introduce a one-parameter
family of random walks which interpolates between the original non-symmetric
random walk...
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