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作者：Wang, Feng-Yu
作者单位：Tianjin University
摘要：In terms of a nice reference probability measure, integrability conditions on the path-dependent drift are presented for (infinite-dimensional) degenerate PDEs to have regular positive solutions. To this end, the corresponding stochastic (partial) differential equations are proved to possess the weak existence and uniqueness of solutions, as well as the existence, uniqueness and entropy estimates of invariant probability measures. When the reference measure satisfies the log-Sobolev inequality...
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作者：Qian, Wei
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：The study of conformal restriction properties in two-dimensions has been initiated by Lawler et al. (J Am Math Soc 16(4):917-955, 2003) who focused on the natural and important chordal case: they characterized and constructed all random subsets of a given simply connected domain that join two marked boundary points and that satisfy the additional restriction property. The radial case (sets joining an inside point to a boundary point) has then been investigated by Wu (Stoch Process Appl 125(2):...
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作者：Berestycki, J.; Fittipaldi, M. C.; Fontbona, J.
作者单位：University of Oxford; Universidad Nacional Autonoma de Mexico; Universidad de Chile; Universidad de Chile
摘要：We introduce flows of branching processes with competition, which describe the evolution of general continuous state branching populations in which interactions between individuals give rise to a negative density dependence term. This generalizes the logistic branching processes studied by Lambert (Ann Appl Probab 15(2):1506-1535, 2005). Following the approach developed by Dawson and Li (Ann Probab 40(2):813-857, 2012), we first construct such processes as the solutions of certain flow of stoc...
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作者：Zhai, Alex
作者单位：Stanford University
摘要：Let X-1, ... , X-n be i.i.d. random vectors in R-d with parallel to X-1 parallel to <= beta. Then, we show that 1/root n (X-1 + ... + X-n) converges to a Gaussian in quadratic transportation (also known as Kantorovich or Wasserstein) distance at a rate of O(root d beta log n/root n), improving a result of Valiant and Valiant. The main feature of our theorem is that the rate of convergence is within log n of optimal for n, d -> infinity.
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作者：Chevyrev, Ilya
作者单位：University of Oxford
摘要：We consider random walks and Levy processes in a homogeneous group G. For all p > 0, we completely characterise (almost) all G-valued Levy processes whose sample paths have finite p-variation, and give sufficient conditions under which a sequence of G-valued random walks converges in law to a Levy process in p-variation topology. In the case that G is the free nilpotent Lie group over R-d, so that processes of finite p-variation are identified with rough paths, we demonstrate applications of o...
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作者：Le Gall, Jean-Francois
作者单位：Universite Paris Saclay
摘要：We discuss subordination of random compact -trees. We focus on the case of the Brownian tree, where the subordination function is given by the past maximum process of Brownian motion indexed by the tree. In that particular case, the subordinate tree is identified as a stable L,vy tree with index 3/2. As a more precise alternative formulation, we show that the maximum process of the Brownian snake is a time change of the height process coding the L,vy tree. We then apply our results to properti...
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作者：Rezaei, Mohammad A.; Zhan, Dapeng
作者单位：Michigan State University
摘要：For a chordal SLE () curve in a domain D, the n-point Green's function valued at distinct points is defined to be here is the Hausdorff dimension of SLE, provided that the limit converges. In this paper, we will show that such Green's functions exist for any finite number of points. Along the way we provide the rate of convergence and modulus of continuity for Green's functions as well. Finally, we give up-to-constant bounds for them.
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作者：Wang, Zhenan
作者单位：University of Washington; University of Washington Seattle
摘要：Under general conditions we show an a priori probabilistic Harnack inequality for the non-negative solution of a stochastic partial differential equation of the following form We also show that the solutions of the above equation are almost surely strictly positive if the initial condition is non-negative and not identically vanishing.
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作者：Hermon, Jonathan; Peres, Yuval
作者单位：University of California System; University of California Berkeley; Microsoft
摘要：There are several works characterizing the total-variation mixing time of a reversible Markov chain in term of natural probabilistic concepts such as stopping times and hitting times. In contrast, there is no known analog for the L-2 mixing time, tau(2) (while there are sophisticated analytic tools to bound tau(2), in general they do not determine tau(2) up to a constant factor and they lack a probabilistic interpretation). In this work we show that tau(2) can be characterized up to a constant...
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作者：De, Anindya; Servedio, Rocco A.
作者单位：Northwestern University; Columbia University
摘要：One of the main results of this paper is a new multidimensional central limit theorem (CLT) for multivariate polynomials under Gaussian inputs. Roughly speaking, the new CLT shows that any collection of Gaussian polynomials with small eigenvalues (suitably defined) must have a joint distribution which is close to a multidimensional Gaussian distribution. The new CLT is proved using tools from Malliavin calculus and Stein's method. A second main result of the paper, which complements the new CL...
