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作者：Horst, Ulrich; Xu, Wei
作者单位：Humboldt University of Berlin; Humboldt University of Berlin
摘要：We provide a general probabilistic framework within which we estab-lish scaling limits for a class of continuous-time stochastic volatility models with self-exciting jump dynamics. In the scaling limit, the joint dynamics of asset returns and volatility is driven by independent Gaussian white noises and two independent Poisson random measures that capture the arrival of exogenous shocks and the arrival of self-excited shocks, respectively. Vari-ous well-studied stochastic volatility models wit...
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作者：Piatnitski, Andrey; Pirogov, Sergey; Zhizhina, Elena
作者单位：UiT The Arctic University of Tromso; Kharkevich Institute for Information Transmission Problems of the RAS; Russian Academy of Sciences
摘要：The paper deals with a family of jump Markov process defined in a medium with a periodic or locally periodic microstructure. We assume that the generator of the process is a zero order convolution type operator with rapidly oscillating locally periodic coefficient and, under natural ellipticity and localization conditions, show that the family satisfies the large deviation principle in the path space equipped with Skorokhod topology. The corre-sponding rate function is defined in terms of a fa...
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作者：Owada, Takashi
作者单位：Purdue University System; Purdue University
摘要：The objective of this paper is to examine the asymptotic behavior of persistence diagrams associated with Cech filtration. A persistence diagram is a graphical descriptor of a topological and algebraic structure of geometric objects. We consider Cech filtration over a scaled random sample r(n)(-1) chi(n) = {r(n)(-1) x(1), ..., r(n)(-1) X-n}, such that r(n) -> 0 as n -> infinity. We treat per- sistence diagrams as a point process and establish their limit theorems in the sparse regime: nr(n)(d)...
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作者：Alberts, Tom; Normand, Raoul
作者单位：Utah System of Higher Education; University of Utah; New York University
摘要：We study the dimension properties of the spectral measure of the circular beta-ensembles. For beta >= 2 it was previously shown by Simon that the spec-tral measure is almost surely singular continuous with respect to Lebesgue measure on partial differential D and the dimension of its support is 1 - 2/beta. We reprove this result with a combination of probabilistic techniques and the so-called Jitomirskaya-Last inequalities. Our method is simpler in nature and mostly self-contained, with an emp...
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作者：Basdevant, Anne-Laure; Gouere, Jean-Baptiste; Theret, Marie
作者单位：Universite de Tours
摘要：We consider the standard model of first-passage percolation on Z(d) (d >= 2), with i.i.d. passage times associated with either the edges or the vertices of the graph. We focus on the particular case where the distribution of the passage times is the Bernoulli distribution with parameter 1 - epsilon. These passage times induce a random pseudo-metric T-epsilon on R-d. By subadditive arguments, it is well known that for any z is an element of R-d \ {0}, the sequence T-epsilon(0, nz)/n converges a...
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作者：Georgiou, Nicholas; Wade, Andrew R.
作者单位：Durham University
摘要：Motivated by nanoscale growth of ultra-thin films, we study a model of deposition, on an interval substrate, of particles that perform Brownian mo-tions until any two meet, when they nucleate to form a static island, which acts as an absorbing barrier to subsequent particles. This is a continuum ver-sion of a lattice model studied in the applied literature. We show that the associated interval-splitting process converges in the sparse deposition limit to a Markovian process (in the vein of Bre...
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作者：Carmona, Rene; Lauriere, Mathieu
作者单位：Princeton University
摘要：We propose two numerical methods for the optimal control of McKean- Vlasov dynamics in finite time horizon. Both methods are based on the intro-duction of a suitable loss function defined over the parameters of a neural net-work. This allows the use of machine learning tools, and efficient implemen-tations of stochastic gradient descent in order to perform the optimization. In the first method, the loss function stems directly from the optimal control problem. The second method tackles a gener...
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作者：Fan, Wai-Tong Louis; Legried, Brandon; ROCH, Sesbastien
作者单位：Indiana University System; Indiana University Bloomington; University of Michigan System; University of Michigan; University of Wisconsin System; University of Wisconsin Madison
摘要：We consider phylogeny estimation under a two-state model of sequence evolution by site substitution on a tree. In the asymptotic regime where the sequence lengths tend to infinity, we show that for any fixed k no statistically consistent phylogeny estimation is possible from k-mer counts over the full leaf sequences alone. Formally, we establish that the joint distribution of k-mer counts over the entire leaf sequences on two distinct trees have total variation distance bounded away from 1 as ...
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作者：Mueller, Carl; Neuman, Eyal
作者单位：University of Rochester; Imperial College London
摘要：We set up an SPDE model for a moving, weakly self-avoiding polymer with intrinsic length J taking values in (0, infinity). Our main result states that the effective radius of the polymer is approximately J5/3; evidently for large J the polymer undergoes stretching. This contrasts with the equilibrium sit-uation without the time variable, where many earlier results show that the effective radius is approximately J.For such a moving polymer taking values in R2, we offer a conjecture that the eff...
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作者：Clark, Jeremy Thane
作者单位：University of Mississippi
摘要：We construct and study a family of random continuum polymer mea-sures Mr corresponding to limiting partition function laws recently derived in a weak-coupling regime for polymer models on hierarchical graphs with marginally relevant disorder. The continuum polymers, which we refer to as directed paths, are identified with isometric embeddings of the unit interval [0, 1] into a compact diamond fractal having Hausdorff dimension two, and there is a natural uniform probability measure, mu, over t...
