اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدMacroscopic stability for nonfinite range kernels
55
0
0.0
(
0
)
تأليف
Tom S. Mountford
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We extend the strong macroscopic stability introduced in Bramson & Mountford (2002) for one-dimensional asymmetric exclusion processes with finite range to a large class of one-dimensional conservative attractive models (including misanthrope process) for which we relax the requirement of finite range kernels. A key motivation is extension of constructive hydrodynamics result of Bahadoran et al. (2002, 2006, 2008) to nonfinite range kernels.
قيم البحث
اقرأ أيضاً
We propose a definition o meta-stability and obtain sufficient conditions for a sequence of Markov processes on finite state spaces to be meta-stable. In the reversible case, these conditions reduce to estimates of the capacity and the measure of cer
tain meta-stable sets. We prove that a class of condensed zero-range processes with asymptotically decreasing jump rates is meta-stable.
Suppose that $gamma$ and $sigma$ are two continuous bounded variation paths which take values in a finite-dimensional inner product space $V$. Recent papers have introduced the truncated and the untruncated signature kernel of $gamma$ and $sigma$, an
d showed how these concepts can be used in classification and prediction tasks involving multivariate time series. In this paper, we introduce general signature kernels and show how they can be interpreted, in many examples, as an average of PDE solutions, and hence how they can be computed using suitable quadrature rules. We extend this analysis to derive closed-form formulae for expressions involving the expected (Stratonovich) signature of Brownian motion. In doing so, we articulate a novel connection between signature kernels and the hyperbolic development map, the latter of which has been a broadly useful tool in the analysis of the signature. As an application we evaluate the use of different general signature kernels as the basis for non-parametric goodness-of-fit tests to Wiener measure on path space.
This paper provides explicit pointwise formulas for the heat kernel on compact metric measure spaces that belong to a $(mathbb{N}timesmathbb{N})$-parameter family of fractals which are regarded as projective limits of metric measure graphs and do not
satisfy the volume doubling property. The formulas are applied to obtain uniform continuity estimates of the heat kernel and to derive an expression of the fundamental solution of the free Schrodinger equation. The results also open up the possibility to approach infinite dimensional spaces based on this model.
We consider the asymptotic behavior of the fluctuations for the empirical measures of interacting particle systems with singular kernels. We prove that the sequence of fluctuation processes converges in distribution to a generalized Ornstein-Uhlenbec
k process. Our result considerably extends classical results to singular kernels, including the Biot-Savart law. The result applies to the point vortex model approximating the 2D incompressible Navier-Stokes equation and the 2D Euler equation. We also obtain Gaussianity and optimal regularity of the limiting Ornstein-Uhlenbeck process. The method relies on the martingale approach and the Donsker-Varadhan variational formula, which transfers the uniform estimate to some exponential integrals. Estimation of those exponential integrals follows by cancellations and combinatorics techniques and is of the type of large deviation principle.
This paper studies transition probabilities from a Borel subset of a Polish space to a product of two Borel subsets of Polish spaces. For such transition probabilities it introduces and studies semi-uniform Feller continuity and a weaker property cal
led WTV-continuity. This paper provides several equivalent definitions of semi-uniform Feller continuity and describes the preservation property of WTV-continuity under integration. The motivation for this study came from the theory of Markov decision processes with incomplete information, and this paper provides fundamental results useful for this theory.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
