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作者：Hairer, Martin; Pillai, Natesh S.
作者单位：University of Warwick; Harvard University
摘要：We consider differential equations driven by rough paths and study the regularity of the laws and their long time behavior. In particular, we focus on the case when the driving noise is a rough path valued fractional Brownian motion with Hurst parameter H is an element of (1/3, 1/2]. Our contribution in this work is twofold. First, when the driving vector fields satisfy Hormander's celebrated Lie bracket condition, we derive explicit quantitative bounds on the inverse of the Malliavin matrix. ...
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作者：Inahama, Yuzuru
作者单位：Nagoya University
摘要：We consider a rough differential equation indexed by a small parameter epsilon > 0. When the rough differential equation is driven by fractional Brownian motion with Hurst parameter H (1/4 < H < 1/2), we prove the Laplace-type asymptotics for the solution as the parameter 8 tends to zero.
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作者：Brieussel, Jeremie
作者单位：Kyoto University
摘要：A variety of behaviors of entropy functions of random walks on finitely generated groups is presented, showing that for any 1/2 <= alpha <= beta <= 1, there is a group Gamma with measure mu equidistributed on a finite generating set such that lim inf log H-Gamma,H-mu(n)/log n = alpha, lim sup H-Gamma,H-mu(n)/log n = beta The groups involved are finitely generated subgroups of the group of automorphisms of an extended rooted tree. The return probability and the drift of a simple random walk Y-n...
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作者：Georgiou, Nicos; Seppaelaeinen, Timo
作者单位：Utah System of Higher Education; University of Utah; University of Wisconsin System; University of Wisconsin Madison
摘要：We study right tail large deviations of the logarithm of the partition function for directed lattice paths in i.i.d. random potentials. The main purpose is the derivation of explicit formulas for the 1 + 1-dimensional exactly solvable case with log-gamma distributed random weights. Along the way we establish some regularity results for this rate function for general distributions in arbitrary dimensions.
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作者：Lyons, Russell
作者单位：Indiana University System; Indiana University Bloomington
摘要：We extend the theory of distance (Brownian) covariance from Euclidean spaces, where it was introduced by Szekely, Rizzo and Bakirov, to general metric spaces. We show that for testing independence, it is necessary and sufficient that the metric space be of strong negative type. In particular, we show that this holds for separable Hilbert spaces, which answers a question of Kosorok. Instead of the manipulations of Fourier transforms used in the original work, we use elementary inequalities for ...
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作者：Berti, Patrizia; Pratelli, Luca; Rigo, Pietro
作者单位：Universita di Modena e Reggio Emilia; University of Pavia
摘要：Let S be a Polish space and (X-n : n >= 1) an exchangeable sequence of S-valued random variables. Let alpha(n)(.) = P(Xn+1 is an element of E . vertical bar X-1, ... X-n) be the preweak dictive measure and a a random probability measure on S such that an alpha(n) -> weak alpha a.s. Two (related) problems are addressed. One is to give conditions for alpha << lambda a.s., where lambda is a (nonrandom) sigma-finite Borel measure on S. Such conditions should concern the finite dimensional distribu...
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作者：Rezakhanlou, Fraydoun
作者单位：University of California System; University of California Berkeley
摘要：The Marcus-Lushnikov process is a simple mean field model of coagulating particles that converges to the homogeneous Smoluchowski equation in the large mass limit. If the coagulation rates grow sufficiently fast as the size of particles get large, giant particles emerge in finite time. This is known as gelation, and such particles are known as gels. Gelation comes in different flavors: simple, instantaneous and complete. In the case of an instantaneous gelation, giant particles are formed in a...
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作者：Basse-O'Connor, Andreas; Rosinski, Jan
作者单位：Aarhus University; University of Tennessee System; University of Tennessee Knoxville
摘要：Let X-n be independent random elements in the Skorohod space D([0, 1]; E) of cadlag functions taking values in a separable Banach space E. Let S-n = Sigma(n)(j=1) X-j. We show that if Sn converges in finite dimensional distributions to a cadlag process, then S-n + y(n) converges a.s. pathwise uniformly over [0, 1], for some y(n) is an element of D([0, 1]; E). This result extends the Ito-Nisio theorem to the space D([0, 1]; E), which is surprisingly lacking in the literature even for E = R. The...
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作者：Roberts, Matthew I.
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：We give short proofs of two classical results about the position of the extremal particle in a branching Brownian motion, one concerning the median position and another the almost sure behaviour.
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作者：Srivastava, Nikhil; Vershynin, Roman
作者单位：Institute for Advanced Study - USA; University of Michigan System; University of Michigan
摘要：We study the minimal sample size N = N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitrary fixed accuracy. We establish the optimal bound N = O(n) for every distribution whose k-dimensional marginals have uniformly bounded 2 + epsilon moments outside the sphere of radius O(root k). In the specific case of log-concave distributions, this result provides an alternative approach to the Kannan-L...
