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作者：Kelly, David; Melbourne, Ian
作者单位：University of North Carolina; University of North Carolina Chapel Hill; New York University; University of Warwick
摘要：Consider an Ito process X satisfying the stochastic differential equation dX = a(X) dt + b(X) dW where a, b are smooth and W is a multidimensional Brownian motion. Suppose that W-n, has smooth sample paths and that Wn converges wealdy to W. A central question in stochastic analysis is to understand the limiting behavior of solutions X-n to the ordinary differential equation dX(n) = a(X-n) dt + b(X-n) dW(n). The classical Wong-Zakai theorem gives sufficient conditions under which X-n converges ...
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作者：Benoist, Yves; Quint, Jean-Francois
作者单位：Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS)
摘要：We prove a central limit theorem for random walks with finite variance on linear groups.
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作者：Fournier, Nicolas; Mischler, Stephane
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite; Universite PSL; Universite Paris-Dauphine
摘要：We consider the (numerically motivated) Nanbu stochastic particle system associated to the spatially homogeneous Boltzmann equation for true hard potentials and Maxwell molecules. We establish a rate of propagation of chaos of the particle system to the unique solution of the Boltzmann equation. More precisely, we estimate the expectation of the squared Wasserstein distance with quadratic cost between the empirical measure of the particle system and the solution to the Boltzmann equation. The ...
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作者：Mukherjee, Chiranjib; Varadhan, S. R. S.
摘要：In proving large deviation estimates, the lower bound for open sets and upper bound for compact sets are essentially local estimates. On the other hand, the upper bound for closed sets is global and compactness of space or an exponential tightness estimate is needed to establish it. In dealing with the occupation measure L-t(A) = 1/t integral(t)(0) 1(A)(W-s) ds of the d-dimensional Brownian motion, which is not positive recurrent, there is no possibility of exponential tightness. The space of ...
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作者：Ortgiese, Marcel; Roberts, Matthew I.
作者单位：University of Munster; University of Bath
摘要：We consider a branching random walk on the lattice, where the branching rates are given by an i.i.d. Pareto random potential. We describe the process, including a detailed shape theorem, in terms of a system of growing lilypads. As an application we show that the branching random walk is intermittent, in the sense that most particles are concentrated on one very small island with large potential. Moreover, we compare the branching random walk to the parabolic Anderson model and observe that al...
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作者：Harris, S. C.; Hesse, M.; Kyprianou, A. E.
作者单位：University of Bath; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We consider a branching Brownian motion with linear drift in which particles are killed on exiting the interval (0, K) and study the evolution of the process on the event of survival as the width of the interval shrinks to the critical value at which survival is no longer possible. We combine spine techniques and a backbone decomposition to obtain exact asymptotics for the near-critical survival probability. This allows us to deduce the existence of a quasi-stationary limit result for the proc...
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作者：Cai, Chunhao; Chigansky, Pavel; Kleptsyna, Marina
作者单位：Nankai University; Hebrew University of Jerusalem; Le Mans Universite
摘要：This paper presents a new approach to the analysis of mixed processes X-t = B-t + G(t), t is an element of [0, T] where B-t is a Brownian motion and G(t) is an independent centered Gaussian process. We obtain a new canonical innovation representation of X, using linear filtering theory. When the kernel K(s,t) = partial derivative(2)/partial derivative s partial derivative t EG(t)G(s,) s not equal t has a weak singularity on the diagonal, our results generalize the classical innovation formulas...
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作者：Bierme, Hermine; Desolneux, Agnes
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Poitiers; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：In this paper, we use the framework of functions of bounded variation and the coarea formula to give an explicit computation for the expectation of the perimeter of excursion sets of shot noise random fields in dimension n >= 1. This will then allow us to derive the asymptotic behavior of these mean perimeters as the intensity of the underlying homogeneous Poisson point process goes to infinity. In particular, we show that two cases occur: we have a Gaussian asymptotic behavior when the kernel...
