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作者：Blath, Jochen; Hammer, Matthias; Ortgiese, Marcel
作者单位：Technical University of Berlin; University of Munster
摘要：The continuous-space symbiotic branching model describes the evolution of two interacting populations that can reproduce locally only in the simultaneous presence of each other. If started with complementary Heaviside initial conditions, the interface where both populations coexist remains compact. Together with a diffusive scaling property, this suggests the presence of an interesting scaling limit. Indeed, in the present paper, we show weak convergence of the diffusively rescaled populations...
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作者：Liechty, Karl; Wang, Dong
作者单位：DePaul University; National University of Singapore
摘要：We consider an ensemble of n nonintersecting Brownian particles on the unit circle with diffusion parameter n(-1/2), which are conditioned to begin at the same point and to return to that point after time T, but otherwise not to intersect. There is a critical value of T which separates the subcritical case, in which it is vanishingly unlikely that the particles wrap around the circle, and the supercritical case, in which particles may wrap around the circle. In this paper, we show that in the ...
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作者：Balan, Raluca M.; Conus, Daniel
作者单位：University of Ottawa; Lehigh University
摘要：In this article, we consider the stochastic wave and heat equations driven by a Gaussian noise which is spatially homogeneous and behaves in time like a fractional Brownian motion with Hurst index H > 1/2. The solutions of these equations are interpreted in the Skorohod sense. Using Malliavin calculus techniques, we obtain an upper bound for the moments of order p >= 2 of the solution. In the case of the wave equation, we derive a Feynman-Kactype formula for the second moment of the solution, ...
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作者：Ekren, Ibrahim; Touzi, Nizar; Zhang, Jianfeng
作者单位：University of Southern California; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：The main objective of this paper and the accompanying one [Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II (2012) Preprint] is to provide a notion of viscosity solutions for fully nonlinear parabolic path-dependent PDEs. Our definition extends our previous work [Ann. Probab. (2014) 42 204-236], focused on the semilinear case, and is crucially based on the nonlinear optimal stopping problem analyzed in [Stochastic Process. Appl. (2014) 124 3277-3311]. We prove that...
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作者：Marko, Roland; Timar, Adam
作者单位：University of Bonn; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
摘要：The allocation problem for a d-dimensional Poisson point process is to find a way to partition the space to parts of equal size, and to assign the parts to the configuration points in a measurable, deterministic (equivariant) way. The goal is to make the diameter R of the part assigned to a configuration point have fast decay. We present an algorithm for d >= 3 that achieves an O(exp(- cR(d))) tail, which is optimal up to c. This improves the best previously known allocation rule, the gravitat...
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作者：Neel, Robert W.; Popescu, Ionel
作者单位：Lehigh University; University System of Georgia; Georgia Institute of Technology; Romanian Academy; Institute of Mathematics of the Romanian Academy
摘要：We develop a stochastic target representation for Ricci flow and normalized Ricci flow on smooth, compact surfaces, analogous to Soner and Touzi's representation of mean curvature flow. We prove a verification/uniqueness theorem, and then consider geometric consequences of this stochastic representation. Based on this stochastic approach, we give a proof that, for surfaces of nonpositive Euler characteristic, the normalized Ricci flow converges to a constant curvature metric exponentially quic...
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作者：Miller, Jason; Watson, Samuel S.; Wilson, David B.
作者单位：Massachusetts Institute of Technology (MIT); Microsoft
摘要：The conformal loop ensemble CLE kappa with parameter 8/3 < kappa < 8 is the canonical conformally invariant measure on countably infinite collections of noncrossing loops in a simply connected domain. Given kappa and nu, we compute the almost-sure Hausdorff dimension of the set of points z for which the number of CLE loops surrounding the disk of radius epsilon centered at z has asymptotic growth nu log(1/epsilon) as epsilon -> 0. By extending these results to a setting in which the loops are ...
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作者：Bertoin, Jean
作者单位：University of Zurich
摘要：A new class of fragmentation-type random processes is introduced, in which, roughly speaking, the accumulation of small dislocations which would instantaneously shatter the mass into dust, is compensated by an adequate dilation of the components. An important feature of these compensated fragmentations is that the dislocation measure nu which governs their evolutions has only to fulfill the integral condition integral P(1 - p(1))(2)nu(dp) < infinity, where p = (p(1),...) denotes a generic mass...
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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.
