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作者：Chen, Zhen-Qing; Fan, Wai-Tong (Louis)
作者单位：University of Washington; University of Washington Seattle; University of North Carolina; University of North Carolina Chapel Hill
摘要：We introduce an interacting particle system in which two families of reflected diffusions interact in a singular manner near a deterministic interface I. This system can be used to model the transport of positive and negative charges in a solar cell or the population dynamics of two segregated species under competition. A related interacting random walk model with discrete state spaces has recently been introduced and studied in Chen and Fan (2014). In this paper, we establish the functional l...
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作者：Kang, Weining; Ramanan, Kavita
作者单位：University System of Maryland; University of Maryland Baltimore; Brown University
摘要：Two frameworks that have been used to characterize reflected diffusions include stochastic differential equations with reflection (SDER) and the so-called submartingale problem. We consider a general formulation of the submartingale problem for (obliquely) reflected diffusions in domains with piecewise C2 boundaries and piecewise continuous reflection vector fields. Under suitable assumptions, we show that well-posedness of the submartingale problem is equivalent to existence and uniqueness in...
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作者：Banuelos, Rodrigo; Davis, Burgess
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作者：Baudoin, Fabrice
作者单位：Purdue University System; Purdue University
摘要：We prove a geometrically meaningful stochastic representation of the derivative of the heat semigroup on sub-Riemannian manifolds with tranverse symmetries. This representation is obtained from the study of Bochner-Weitzenbock type formulas for sub-Laplacians on 1-forms. As a consequence, we prove new hypoelliptic heat semigroup gradient bounds under natural global geometric conditions. The results are new even in the case of the Heisenberg group which is the simplest example of a sub-Riemanni...
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作者：Eisenbaum, Nathalie
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
摘要：A permanental vector with a symmetric kernel and index 2 is a squared Gaussian vector. The definition of permanental vectors is a natural extension of the definition of squared Gaussian vectors to nonsymmetric kernels and to positive indexes. The only known permanental vectors either have a positive definite kernel or are infinitely divisible. Are there some others? We present a partial answer to this question.
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作者：Nualart, David; Tudor, Ciprian A.
作者单位：University of Kansas; Universite de Lille; Bucharest University of Economic Studies
摘要：The aim of this paper is to show an estimate for the determinant of the covariance of a two-dimensional vector of multiple stochastic integrals of the same order in terms of a linear combination of the expectation of the determinant of its iterated Malliavin matrices. As an application, we show that the vector is not absolutely continuous if and only if its components are proportional.
