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作者：Glatt-Holtz, Nathan E.; Vicol, Vlad C.
作者单位：Indiana University System; Indiana University Bloomington; University of Chicago
摘要：We establish the local existence of pathwise solutions for the stochastic Euler equations in a three-dimensional bounded domain with slip boundary conditions and a suitable nonlinear multiplicative noise. In the two-dimensional case we obtain the global existence of these solutions with additive or linear-multiplicative noise. Finally, we show that, in the three-dimensional case, the addition of linear multiplicative noise provides a regularizing effect; the global existence of solutions occur...
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作者：Lalley, Steven P.; Perkins, Edwin A.; Zheng, Xinghua
作者单位：University of Chicago; University of British Columbia; Hong Kong University of Science & Technology
摘要：We consider measure-valued processes X = (X-t) that solve the following martingale problem: for a given initial measure X-0, and for all smooth, compactly supported test functions phi, X-t(phi) = X-0(phi) + 1/2 integral(t)(0)Xs(Delta phi) ds + 1/2 integral(t)(0) Xs (phi) ds -integral(t)(0)Xs(L-s phi) ds + M-t(phi) Here Ls(x) is the local time density process associated with X, and Mt (co) is a martingale with quadratic variation [M-t(phi)](t) =integral(t)(0)Xs(phi(2)) ds. Such processes arise ...
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作者：Goetze, Friedrich; Zaitsev, Andrei Yu
作者单位：University of Bielefeld; Russian Academy of Sciences; St. Petersburg Scientific Centre of the 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
摘要：Let X, X-1, X-2,... be i.i.d. R-d-valued real random vectors. Assume that EX = 0, cov X = C, E vertical bar vertical bar X vertical bar vertical bar(2) = sigma(2) and that X is not concentrated in a proper subspace of R-d Let G be a mean zero Gaussian random vector with the same covariance operator as that of X. We study the distributions of nondegenerate quadratic forms Q[S-N] of the normalized sums S-N = N-(1/2) (X-1 +...+ X-N) and show that, without any additional conditions, Delta(N) =(def...
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作者：Hu, Yaozhong; Nualart, David; Xu, Fangjun
作者单位：University of Kansas; East China Normal University
摘要：We prove a central limit theorem for an additive functional of the d-dimensional fractional Brownian motion with Hurst index H is an element of (1/1+d, 1/d), using the method of moments, extending the result by Papanicolaou, Stroock and Varadhan in the case of the standard Brownian motion.
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作者：Nguyen, Hoi H.; Van Vu
作者单位：University System of Ohio; Ohio State University; Yale University
摘要：Let A(n) be an n by n random matrix whose entries are independent real random variables with mean zero, variance one and with subexponential tail. We show that the logarithm of vertical bar det A(n)vertical bar I satisfies a central limit theorem. More precisely, [GRAPHICS] .
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作者：Berger, Noam; Borgs, Christian; Chayes, Jennifer T.; Saberi, Amin
作者单位：Hebrew University of Jerusalem; Microsoft; Stanford University
摘要：We give an explicit construction of the weak local limit of a class of preferential attachment graphs. This limit contains all local information and allows several computations that are otherwise hard, for example, joint degree distributions and, more generally, the limiting distribution of subgraphs in balls of any given radius k around a random vertex in the preferential attachment graph. We also establish the finite-volume corrections which give the approach to the limit.
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作者：Kyprianou, Andreas E.; Carlos Pardo, Juan; Watson, Alexander R.
作者单位：University of Bath; CIMAT - Centro de Investigacion en Matematicas
摘要：We consider two first passage problems for stable processes, not necessarily symmetric, in one dimension. We make use of a novel method of path. censoring in order to deduce explicit formulas for hitting probabilities, hitting distributions and a killed potential measure. To do this, we describe in full detail the Wiener-Hopf factorization of a new Lamperti-stable-type Levy process obtained via the Lamperti transform, in the style of recent work in this area.
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作者：Li, Zenghu
作者单位：Beijing Normal University
摘要：A family of continuous-state branching processes with immigration are constructed as the solution flow of a stochastic equation system driven by time space noises. The family can be regarded as an inhomogeneous increasing path-valued branching process with immigration. Two nonlocal branching immigration superprocesses can be defined from the flow. We identify explicitly the branching and immigration mechanisms of those processes. The results provide new perspectives into the tree-valued Markov...
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作者：Ekren, Ibrahim; Keller, Christian; Touzi, Nizar; Zhang, Jianfeng
作者单位：University of Southern California; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：In this paper we propose a notion of viscosity solutions for path dependent semi-linear parabolic PDEs. This can also be viewed as viscosity solutions of non-Markovian backward SDEs, and thus extends the well-known nonlinear Feynman-Kac formula to non-Markovian case. We shall prove the existence, uniqueness, stability and comparison principle for the viscosity solutions. The key ingredient of our approach is a functional Ito calculus recently introduced by Dupire [Functional Ito calculus (2009...
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作者：Tsirelson, Boris
作者单位：Tel Aviv University
摘要：A noise is a kind of homomorphism from a Boolean algebra of domains to the lattice of sigma-fields. Leaving aside the homomorphism we examine its image, a Boolean algebra of sigma-fields. The largest extension of such Boolean algebra of sigma-fields, being well-defined always, is a complete Boolean algebra if and only if the noise is classical, which answers an old question of J. Feldman.
