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作者：Lalley, SP; Sellke, T
作者单位：Purdue University System; Purdue University
摘要：A conjecture of Liggett concerning the regime of weak survival for the contact process on a homogeneous tree is proved. The conjecture is shown to imply that the Hausdorff dimension of the limit set of such a contact process is no larger than half the Hausdorff dimension of the space of ends of the tree. The conjecture is also shown to imply that at the boundary between weak survival and strong survival, the contact process survives only weakly, a theorem previously proved by Zhang. Finally, a...
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作者：Grigor'yan, A; Kelbert, M
作者单位：Imperial College London
摘要：We investigate the escape rate of the Brownian motion W-x(t) on a complete noncompact Riemannian manifold. Assuming that the manifold has at most polynomial volume growth and that its Ricci curvature is bounded below, we prove that dist(W-x(t), x) less than or equal to root Ct log t for all large t with probability 1. On the other hand, if the Ricci curvature is nonnegative and the volume growth is at least polynomial of the order n > 2, then dist(W-x(t), x) greater than or equal to root Ct/lo...
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作者：Dawson, DA; Perkins, EA
作者单位：University of British Columbia
摘要：We study a system of two interacting populations which undergo random migration and mutually catalytic branching. The branching rate of one population at a site is proportional to the mass of the other population at the site. The system is modelled by an infinite system of stochastic differential equations, allowing symmetric Markov migration, if the set of sites is discrete (Z(d)), or by a stochastic partial differential equation with Brownian migration if the set of sites is the real line. A...
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作者：Wehr, J; Woo, J
作者单位：University of Arizona; University of Arizona
摘要：An H-geodesic is a doubly infinite path which locally minimizes the passage time in the i.i.d. first passage percolation model on a half-plane H. Under the assumption that the bond passage times are continuously distributed with a finite mean, we prove that, with probability 1, H-geodesics do not exist. As a corollary we show that, with probability 1, any geodesic in the analogous model on the whole plane Z(2) has to intersect all straight lines with rational slopes.
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作者：Adelman, O; Burdzy, K; Pemantle, R
作者单位：Sorbonne Universite; University of Washington; University of Washington Seattle; University of Wisconsin System; University of Wisconsin Madison
摘要：A fixed two-dimensional projection of a three-dimensional Brownian motion is almost surely neighborhood recurrent; is this simultaneously true of all the two-dimensional projections with probability 1? Equivalently: three-dimensional Brownian motion hits any infinite cylinder with probability 1; does it hit all cylinders? This papers shows that the answer is no. Brownian motion in three dimensions avoids random cylinders and in fact avoids bodies of revolution that grow almost as fast as cones.
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作者：Hambly, BM; Lyons, TJ
作者单位：University of Edinburgh; Imperial College London
摘要：We construct a Levy stochastic area for Brownian motion on the Sierpinski gasket. The standard approach via Ito integrals fails because this diffusion has sample paths which are far rougher than those of semimartingales. We thus provide an example demonstrating the restrictions of the semimartingale framework. As a consequence of the existence of the area one has a stochastic calculus and can solve stochastic differential equations driven by Brownian motion on the Sierpinski gasket.
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作者：Perera, G; Wschebor, M
作者单位：Universite Paris Saclay; Universidad de la Republica, Uruguay
摘要：We show that 1/root epsilon {integral(-infinity)(infinity) f(u)k(epsilon)N(tau)(X epsilon)(u) du - integral(0)(tau) f(X-t)a(t)dt} converges in law (as a continuous process) to c(psi) f(0)(tau) f(X-t)a(t) dB(t), where X-t = integral(0)(t) a(s) dW(s) + integral(0)(t) b(s) ds, with W a standard Brownian motion, a. and b regular and adapted processes, X-epsilon(t) = integral(-infinity)(infinity)(1/epsilon)psi((t - u)/epsilon)X-u du, psi a smooth kernel, N-t(g)(u) the number of roots of the equatio...
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作者：Qian, J
作者单位：Bucknell University
摘要：The p-variation of a function f is the supremum of the sums of the pth powers of absolute increments of f over nonoverlapping intervals. Let F be a continuous probability distribution function. Dudley has shown that the p-variation of the empirical process is bounded in probability as n --> infinity if and only if p > 2, and for 1 less than or equal to p less than or equal to 2, the p-variation of the empirical process is at least n(1-p/2) and is at most of the order n(1-p/2)(log log n)(p/2) i...
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作者：Choulli, T; Krawczyk, L; Stricker, C
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Marie et Louis Pasteur; University of Warsaw
摘要：After introducing a new concept, the notion of E-martingale, we extend the well-known Doob inequality (for 1 < p < + infinity) and the Burkholder-Davis-Gundy inequalities (for p = 2) to E-martingales. By means of these inequalities, we give sufficient conditions for the closedness of a space of stochastic integrals with respect to a fixed R-d-valued semimartingale, a question which arises naturally in the applications to financial mathematics. We also provide a necessary and sufficient conditi...
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作者：Leon, JA; Nualart, D
作者单位：Instituto Politecnico Nacional - Mexico; CINVESTAV - Centro de Investigacion y de Estudios Avanzados del Instituto Politecnico Nacional; University of Barcelona
摘要：We prove the existence of a unique mild solution for a stochastic evolution equation on a Hilbert space driven by a cylindrical Wiener process. The generator of the corresponding evolution system is supposed to be random and adapted to the filtration generated by the Wiener process. The proof is based on a maximal inequality for the Skorohod integral deduced from the Ito's formula for this anticipating stochastic integral.
