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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：Avena, Luca; Bolthausen, Erwin; Ritzmann, Christine
作者单位：Leiden University; Leiden University - Excl LUMC; University of Zurich
摘要：We prove error bounds in a central limit theorem for solutions of certain convolution equations. The main motivation for investigating these equations stems from applications to lace expansions, in particular to weakly self-avoiding random walks in high dimensions. As an application we treat such self-avoiding walks in continuous space. The bounds obtained are sharper than those obtained by other methods.
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作者：Chelkak, Dmitry
作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Scientific Centre of the Russian Academy of Sciences; Saint Petersburg State University; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We prove a number of double-sided estimates relating discrete counterparts of several classical conformal invariants of a quadrilateral: cross-ratios, extremal lengths and random walk partition functions. The results hold true for any simply connected discrete domain Omega with four marked boundary vertices and are uniform with respect to Omega's which can be very rough, having many fiords and bottlenecks of various widths. Moreover, due to results from [Boundaries of planar graphs, via circle...
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作者：Gonzales-Gargate, Ivan I.; Ruffino, Paulo R.
作者单位：Universidade Estadual de Campinas
摘要：Consider an SDE on a foliated manifold whose trajectories lay on compact leaves. We investigate the effective behavior of a small transversal perturbation of order epsilon. An average principle is shown to hold such that the component transversal to the leaves converges to the solution of a deterministic ODE, according to the average of the perturbing vector field with respect to invariant measures on the leaves, as a goes to zero. An estimate of the rate of convergence is given. These results...
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作者：Hillion, Erwan; Johnson, Oliver
作者单位：University of Luxembourg; Aix-Marseille Universite; University of Bristol
摘要：We introduce a framework to consider transport problems for integer-valued random variables. We introduce weighting coefficients which allow us to characterize transport problems in a gradient flow setting, and form the basis of our introduction of a discrete version of the Benamou-Brenier formula. Further, we use these coefficients to state a new form of weighted log-concavity. These results are applied to prove the monotone case of the Shepp-Olkin entropy concavity conjecture.
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作者：Beiglboeck, Mathias; Juillet, Nicolas
作者单位：University of Vienna; Universites de Strasbourg Etablissements Associes; Universite de Strasbourg; Centre National de la Recherche Scientifique (CNRS); Universites de Strasbourg Etablissements Associes; Universite de Strasbourg
摘要：The basic problem of optimal transportation consists in minimizing the expected costs E[c(X-1, X-2)] by varying the joint distribution (X-1, X-2) where the marginal distributions of the random variables X-1 and X-2 are fixed. Inspired by recent applications in mathematical finance and connections with the peacock problem, we study this problem under the additional condition that (X-i)(i=1,2) is a martingale, that is, E[X-2 vertical bar X-1] = X-1. We establish a variational principle for this ...
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作者：Lee, James R.; Peres, Yuval; Smart, Charles K.
作者单位：University of Washington; University of Washington Seattle; Microsoft; University of Chicago
摘要：Consider a discrete-time martingale {X-t} taking values in a Hilbert space H. We show that if for some L >= 1, the bounds E[parallel to Xt+1 - X-t parallel to(2)(H)parallel to X-t] = 1 and parallel to Xt+1 - Xt+1 parallel to(H) <= L are satisfied for all times t >= 0, then there is a constant c = c(L) such that for 1 <= R <= root t, P(parallel to X-t-X0 parallel to(H) <= R) <= cR/root t . Following Lee and Peres [Ann. Probab. 41(2013) 3392-3419], this estimate has applications to small-ball es...
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作者：Xie, Longjie; Zhang, Xicheng
作者单位：Wuhan University
摘要：By establishing a characterization for Sobolev differentiability of random fields, we prove the weak differentiability of solutions to stochastic differential equations with local Sobolev and super-linear growth coefficients with respect to the starting point. Moreover, we also study the strong Feller property and the irreducibility to the associated diffusion semigroup.
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作者：Pekoz, Erol A.; Rollin, Adrian; Ross, Nathan
作者单位：Boston University; National University of Singapore; University of Melbourne
摘要：We study a new class of time inhomogeneous Polya-type urn schemes and give optimal rates of convergence for the distribution of the properly scaled number of balls of a given color to nearly the full class of generalized gamma distributions with integer parameters, a class which includes the Rayleigh, half-normal and gamma distributions. Our main tool is Stein's method combined with characterizing the generalized gamma limiting distributions as fixed points of distributional transformations re...
