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作者：Jacod, J; Protter, P
作者单位：Sorbonne Universite; Purdue University System; Purdue University
摘要：We are interested in the rate of convergence of the Euler scheme approximation of the solution to a stochastic differential equation driven by a general (possibly discontinuous) semimartingale, and by the asymptotic behavior of the associated normalized error. It is well known that for Ito's equations the rate is 1/root n;we provide a necessary and sufficient condition for this rate to be 1 root n when the driving semimartingale is a continuous martingale, or a continuous semimartingale under ...
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作者：Goldman, PA
作者单位：Universite Claude Bernard Lyon 1
摘要：In connection with a conjecture stated by D. G. Kendall in the forties, we describe the asymptotic behavior of the distribution function of the area of the planar Crofton cell. We deduce from this (in support of his conjecture) that expressed in terms of eigenvalues, the large Crofton cells are nearly circular. We obtain also the asymptotic behavior of the Laplace transform of the law of the perimeter of the convex hull of planar Brownian motion run until time 1. This last result implies that ...
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作者：Enchev, OB
作者单位：Boston University
摘要：Given a Riemannian manifold M and loop phi: S-1 bar right arrow M, we construct a Gaussian random process S-1 There Exists theta curved right arrow X-theta epsilon T-phi(theta)M, which is an analog of the Brownian motion process in the sense that the formal covariant derivative theta curved right arrow del(theta)X(theta) appears as a stationary process whose spectral measure is uniformly distributed over some discrete set. We show that X satisfies the two-point Markov property (reciprocal proc...
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作者：Aldous, D; Pitman, J
作者单位：University of California System; University of California Berkeley
摘要：Regard an element of the set Delta := {(x(1), x(2), ...): x(1) greater than or equal to x(2) greater than or equal to ... greater than or equal to 0, Sigma(i) x(i) = 1} as a fragmentation of unit mass into clusters of masses x(i). The additive coalescent of Evans and Pitman is the Delta-valued Markov process in which pairs of clusters of masses {x(i), x(j)} merge into a cluster of mass x(i) + x(j) at rate x(i) + x(j). They showed that a version (X-infinity(t), -infinity < t < infinity) of this...
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作者：Mytnik, L
作者单位：University of British Columbia
摘要：The uniqueness in law for the equation partial derivative X-t/partial derivative t = 1/2 Delta X-t + X-t(gamma)(W) over dot is established for 1/2 < gamma < 1. The proof uses a duality technique and requires the construction of an approximating sequence of dual processes.
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作者：Hoffman, C
作者单位：University System of Maryland; University of Maryland College Park
摘要：Benjamini, Pemantle and Peres constructed nearest neighbor processes which have predictability profiles that decay faster than that of the simple random walk. Haggstrom and Mossel found processes with even faster decaying predictability profiles. We prove that the rate of decay achieved by Haggstrom and Mossel is optimal.
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作者：Li, SM; Ogura, Y
作者单位：Saga University
摘要：The purpose of this paper is to prove some convergence theorems of closed and convex set valued sub- and supermartingales in the Kuratowski-Mosco sense. To get submartingale convergence theorems, we give sufficient conditions for the Kudo-Aumann integral and Hiai-Umegaki conditional expectation to be closed both for compact convex set valued random variables and for closed convex set valued random variables. We also give an example of a bounded closed convex set valued random variable whose Ku...
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作者：Bertoin, J
作者单位：Sorbonne Universite
摘要：Let xi, xi(1), be i.i.d. real-valued random variables and S-n = xi(1) + ... + xi(n). In the case when the distribution of xi is close to a stable (alpha) law for some alpha is an element of (0, 1) boolean OR (1, 2), we investigate the asymptotic behavior in distribution of the maximum of normalized sums, max(k = 1, ..., n) k(-1/alpha) S-k. This completes the Darling-Erdos limit theorem for the case alpha = 2.
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作者：Mohammed, SEA; Scheutzow, MKR
作者单位：Southern Illinois University System; Southern Illinois University; Technical University of Berlin
摘要：We study the behavior for large \x\ of Kunita-type stochastic flows phi(t, omega, x) on R-d, driven by continuous spatial semimartingales. For this class of flows we prove new spatial estimates for large \x\, under very mild regularity conditions on the driving semimartingale random field. It is expected that the results would be of interest for the theory of stochastic flows on noncompact manifolds as well as in the study of nonlinear filtering, stochastic functional and partial differential ...
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作者：Deuschel, JD; Rosen, J
作者单位：Technical University of Berlin; City University of New York (CUNY) System; College of Staten Island (CUNY)
摘要：We derive a large deviation principle for the occupation time functional, acting on functions with zero Lebesgue integral, for both super-Brownian motion and critical branching Brownian motion in three dimensions. Our technique, based on a moment formula of Dynkin, allows us to compute the exact rate functions, which differ for the two processes. Obtaining the exact rate function for the super-Brownian motion solves a conjecture of Lee and Remillard. We also show the corresponding CLT and obta...
