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作者：Jentzen, Arnulf; Kloeden, Peter
作者单位：Goethe University Frankfurt
摘要：The solution of a parabolic stochastic partial differential equation (SPDE) driven by an infinite-dimensional Brownian motion is in general not a semi-martingale anymore and does in general not satisfy an Ito formula like the solution of a finite-dimensional stochastic ordinary differential equation (SODE). In particular, it is not possible to derive stochastic Taylor expansions as for the solution of a SODE using an iterated application of the Ito formula. Consequently, until recently, only l...
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作者：Atar, Rami; Budhiraja, Amarjit
作者单位：Technion Israel Institute of Technology; University of North Carolina; University of North Carolina Chapel Hill
摘要：Given a bounded C(2) domain G subset of R(m), functions g is an element of C(partial derivative G, R) and h is an element of C((G) over bar, R backslash {0}), let u denote the unique viscosity solution to the equation -2 Delta(infinity)u = h in G with boundary data g. We provide a representation for u as the value of a two-player zero-sum stochastic differential game.
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作者：Windisch, David
作者单位：Weizmann Institute of Science
摘要：Following the recent work of Sznitman [Probab. Theory Related Fields 145 (2009) 143-174], we investigate the microscopic picture induced by a random walk trajectory on a cylinder of the form G(N) x Z, where G(N) is a large finite connected weighted graph, and relate it to the model of random interlacements on infinite transient weighted graphs. Under suitable assumptions, the set of points not visited by the random walk until a time of order vertical bar G(N)vertical bar(2) in a neighborhood o...
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作者：Hu, Xiaoyu; Miller, Jason; Peres, Yuval
作者单位：Chinese Academy of Sciences; Stanford University; Microsoft
摘要：Let U subset of C be a bounded domain with smooth boundary and let F be an instance of the continuum Gaussian free field on U with respect to the Dirichlet inner product integral(U) del f(x).del g(x)dx. The set T (a; U) of a-thick points of F consists of those z is an element of U such that the average of F on a disk of radius r centered at z has growth root a/pi log 1/r as r -> 0. We show that for each 0 <= a <= 2 the Hausdorff dimension of T (a; U) is almost surely 2 - a, that nu(2-a)(T (a; ...
