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作者：Bergenthum, Jan; Ruedschendorf, Ludger
作者单位：University of Freiburg
摘要：In this paper, we derive comparison results for terminal values of d-dimensional special semimartingales and also for finite-dimensional distributions of multivariate Levy processes. The comparison is with respect to nondecreasing, (increasing) convex, (increasing) directionally convex and (increasing) supermodular functions. We use three different approaches. In the first approach, we give sufficient conditions on the local predictable characteristics that imply ordering of terminal values of...
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作者：Foss, Serguei; Korshunov, Dmitry
作者单位：Heriot Watt University
摘要：Suppose F is a distribution on the half-line [0, infinity). We study the limits of the ratios of tails F * F(x) vertical bar F(x) as x -> infinity. We also discuss the classes of distributions s, s(y) and s*.
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作者：Ben Arous, Gerard; Cerny, Jiri
作者单位：New York University; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
摘要：We give the quenched scaling limit of Bouchaud's trap model in d >= 2. This scaling limit is the fractional-kinetics process, that is the time change of a d-dimensional Brownian motion by the inverse of an independent alpha-stable subordinator.
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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：Bass, Richard F.; Burdzy, Krzysztof; Chen, Zhen-Qing
作者单位：University of Connecticut; University of Washington; University of Washington Seattle
摘要：We introduce a new method of proving pathwise uniqueness, and we apply it to the degenerate stochastic differential equation dX(t) = vertical bar X-t vertical bar(alpha) dW(t), where W-t is a one-dimensional Brownian motion and alpha is an element of (0, 1/2). Weak uniqueness does not hold for the solution to this equation. If one restricts attention, however, to those solutions that spend zero time at 0, then pathwise uniqueness does hold and a strong solution exists. We also consider a class...
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作者：Baik, Jinho; Suidan, Toufic M.
作者单位：University of Michigan System; University of Michigan; University of California System; University of California Santa Cruz
摘要：We consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function. We prove that in a certain limiting regime where the number of walks and the number of time steps grow to infinity, several limiting distributions of the walks at the mid-time behave as the eigenvalues of random Hermitian matrices as the dimension of the matrices grows to infinity.
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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...
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作者：Kruk, Lukasz; Lehoczky, John; Ramanan, Kavita; Shreve, Steven
作者单位：Maria Curie-Sklodowska University; Carnegie Mellon University; Carnegie Mellon University
摘要：The Skorokhod map is a convenient tool for constructing solutions to stochastic differential equations with reflecting boundary conditions. In this work, an explicit formula for the Skorokhod map Gamma(0,a) on [0,a] for any a > 0 is derived. Specifically, it is shown that on the space D[0, infinity) of right-continuous functions with left limits taking values in R, Gamma (0, a) = Lambda(a) omicron Gamma(0), where Lambda(a) : D[0, infinity) -> D [0, infinity) is defined by [Graphics] and Gamma(...
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作者：Turner, Amanda G.
作者单位：University of Cambridge
摘要：We consider sequences (X-t(N))t >= 0 of Markov processes in two dimensions whose fluid limit is a stable solution of an ordinary differential equation of the form x(t) = b(x(t)), where b(x) = ((-mu)(0)(0)(lambda))x + tau(x) for some lambda, mu > 0 and tau(x) = 0(vertical bar x vertical bar(2)). Here the processes are indexed so that the variance of the fluctuations of X-t(N) is inversely proportional to N. The simplest example t arises from the OK Corral gunfight model which was formulated by ...
