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作者：Nishiyama, Yoichi
作者单位：Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
摘要：This note extends some results of Nishiyama [Ann. Probab. 28 (2000) 685-712]. A maximal inequality for stochastic integrals with respect to integer-valued random measures which may have infinitely many jumps on compact time intervals is given. By using it, a tightness criterion is obtained; if the so-called quadratic modulus is bounded in probability and if a certain entropy condition on the parameter space is satisfied, then the tightness follows. Our approach is based on the entropy techniqu...
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作者：Randrianantoanina, Narcisse
作者单位：University System of Ohio; Miami University
摘要：We prove a weak-type (1, 1) inequality involving conditioned versions of square functions for martingales in noncommutative L-P-spaces associated with finite von Neumann algebras. As application, we determine the optimal orders for the best constants in the noncommutative Burkholder/Rosenthal inequalities from [Ann. Probab. 31 (2003) 948-995]. We also discuss BMO-norms of sums of noncommuting order-independent operators.
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作者：Ferrari, Pablo A.; Martin, James B.
作者单位：Universidade de Sao Paulo; University of Oxford
摘要：We consider totally asymmetric simple exclusion processes with n types of particle and holes (n-TASEPs) on Z and on the cycle Z(N). Angel recently gave an elegant construction of the stationary measures for the 2-TASEP, based on a pair of independent product measures. We show that Angel's construction can be interpreted in terms of the operation of a discrete-time M/M/1 queueing server; the two product measures correspond to the arrival and service processes of the queue. We extend this constr...
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作者：Kendall, Wilfrid S.
作者单位：University of Warwick
摘要：It is shown how to construct a successful co-adapted coupling of two copies of an n-dimensional Brownian motion (B-1,..., B-n) while simultaneously coupling all corresponding copies of Levy stochastic areas integral B-i d B-j - integral B-j dB(i). It is conjectured that successful co-adapted couplings still exist when the Levy stochastic areas are replaced by a finite set of multiply iterated path- and time-integrals, subject to algebraic compatibility of the initial conditions.
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作者：Liggett, Thomas M.; Steif, Jeffrey E.; Toth, Balint
作者单位：University of California System; University of California Los Angeles; Chalmers University of Technology; University of Gothenburg
摘要：We show that a large collection of statistical mechanical systems with quadratically represented Hamiltonians on the complete graph can be extended to infinite exchangeable processes. This extends a known result for the ferromagnetic Curie-Weiss Ising model and includes as well all ferromagnetic Curie-Weiss Potts and Curie-Weiss Heisenberg models. By de Finetti's theorem, this is equivalent to showing that these probability measures can be expressed as averages of product measures. We provide ...
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作者：Shi, Zhan; Zindy, Olivier
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：Sinai's walk is a recurrent one-dimensional nearest-neighbor random walk in random environment. It is known for a phenomenon of strong localization, namely, the walk spends almost all time at or near the bottom of deep valleys of the potential. Our main result shows a weakness of this localization phenomenon: with probability one, the zones where the walk stays for the most time can be far away from the sites where the walk spends the most time. In particular, this gives a negative answer to a...
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作者：Coutin, Laure; Friz, Peter; Victoir, Nicolas
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; University of Cambridge; University of Oxford
摘要：We consider anticipative Stratonovich stochastic differential equations driven by Some stochastic process lifted to a rough path. Neither adaptedness of initial point and vector fields nor commuting conditions between vector field is assumed. Under a simple condition on the stochastic process, we show that the unique solution of the above SDE understood in the rough path sense is actually a Stratonovich solution. We then show that this condition is satisfied by the Brownian motion. As applicat...
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作者：Chen, Xia
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：We study the upper tail behaviors of the local times of the additive Levy processes and additive random walks. The limit forms we establish are the moderate deviations and the laws of the iterated logarithm for the L-2-norms of the local times and for the local times at a fixed site.
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作者：Popier, A.
作者单位：Aix-Marseille Universite
摘要：In this paper. we are concerned with one-dimensional backward stochastic differential equations (BSDE in short) of the following type: Y-t = xi - integral(tau)(t Lambda tau) Y-r vertical bar Y-r vertical bar(q) dr - integral(tau)(t Lambda tau) Z(r) d B-r, t >= 0, where tau is a stopping time, q is a positive constant and xi is a F-tau-measurable random variable such that P(xi = +infinity) > 0. We study the link between these BSDE and the Dirichlet problem on a domain D subset of R-d and with b...
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作者：Eisenbaum, Nathalie; Kaspi, Haya
作者单位：Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Technion Israel Institute of Technology
摘要：The problem of finding a necessary and sufficient condition for the continuity of the local times for a general Markov process is still open. Barlow and Hawkes have completely treated the case of the Levy processes, and Marcus and Rosen have solved the case of the strongly symmetric Markov processes. We treat here the continuity of the local times of Borel right processes. Our approach unifies that of Barlow and Hawkes and of Marcus and Rosen, by using an associated Gaussian process, that appe...
