Related papers: On the planar Brownian Green's function for stoppi…
We define and prove the existence of a fractional Brownian motion indexed by a collection of closed subsets of a measure space. This process is a generalization of the set-indexed Brownian motion, when the condition of independance is…
We construct the Green function for second-order elliptic equations in non-divergence form when the mean oscillations of the coefficients satisfy the Dini condition. We show that the Green's function is BMO in the domain and establish…
Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two…
We conduct an investigation of the differentiability and continuity of reward functionals associated to Markovian randomized stopping times. Our focus is mostly on the differentiability, which is a crucial ingredient for a common approach…
This paper investigates the multitime linear normal PDE systems. We study especially the controllability of such systems, obtaining complementary results to those in our recent papers. Here the multitime controllability original results are…
Using the Gegenbauer polynomials and the zonal harmonics functions we give some representation formula of the Green function in the annulus. We apply this result to prove some uniqueness results for some nonlinear elliptic problems.
We compute, at two-loop order, one-particle-irreducible Green functions and effective action in noncommutative $\lambda[\Phi^3]_\star$-theory for both planar (g=0, h=3) and nonplanar (g=1, h=1) contributions. We adopt worldline formulation…
We study the asymptotic behaviour of a properly normalized time-changed multidimensional Wiener process; the time change is given by an additive functional of the Wiener process itself. At the level of generators, the time change means that…
In this article, we study the family of probability measures (indexed by a positive real number t), obtained by penalization of the Brownian motion by a given functional of its local times at time t. We prove that this family tends to a…
We study Green functions for stationary Stokes systems satisfying the conormal derivative boundary condition. We establish existence, uniqueness, and various estimates for the Green function under the assumption that weak solutions of the…
We consider a fractional Brownian motion with unknown linear drift such that the drift coefficient has a prior normal distribution and construct a sequential test for the hypothesis that the drift is positive versus the alternative that it…
Quantization of electrodynamics in curved space-time in the Lorenz gauge and with arbitrary gauge parameter makes it necessary to study Green functions of non-minimal operators with variable coefficients. Starting from the integral…
We present a high order numerical method for the solution of the Neumann Green's function in two dimensions. For a general closed planar curve, our computational method resolves both the interior and exterior Green's functions with the…
The balance held by Brownian motion between temporal regularity and randomness is embodied in a remarkable way by Levy's forgery of continuous functions. Here we describe how this property can be extended to forge arbitrary dependences…
The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…
We study a continuous pathwise local time of order p for continuous functions with finite p-th variation along a sequence of time partitions, for even integers p >= 2. With this notion, we establish a Tanaka-type change of variable formula,…
Starting with conformally covariant correlation functions, a sequence of functional representations of the conformal algebra is constructed. A key step is the introduction of representations which involve an auxiliary functional. It is…
We prove the central limit theorem of random variables induced by distances to Brownian paths and Green functions on the universal cover of Riemannian manifolds of finite volume with pinched negative curvature. We further provide some…
We present a rather unknown version of the change of variables formula for non-autonomous functions. We will show that this formula is equivalent to Green's Theorem for regions of the plane bounded by the graphs of two continuously…
In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…