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作者：Roy, Emmanuel
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris 13
摘要：We show that a stationary IDp process (i.e., an infinitely divisible stationary process without Gaussian part) can be written as the independent sum of four stationary IDp processes, each of them belonging to a different class characterized by its Levy measure. The ergodic properties of each class are, respectively, nonergodicity, weak mixing, mixing of all order and Bernoullicity. To obtain these results, we use the representation of an IDp process as an integral with respect to a Poisson mea...
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作者：Du Toit, J.; Peskir, G.
作者单位：University of Witwatersrand; University of Manchester
摘要：Given a standard Brownian motion B-mu = (B-t(mu))(0 <= t <= T) with drift mu is an element of R and letting S-t(mu) = max(0 <= s <= t) B-s(mu) for 0 <= t <= T, we consider the optimal prediction problem: V = inf (0 <=tau <= T) E(B-tau(mu) - S-T(mu))(2) where the infimum is taken over all stopping times tau of B-mu. Reducing the optimal prediction problem to a parabolic free-boundary problem we show that the following stopping time is optimal: tau(*) = inf{t(*) <= t <= T vertical bar b(1) (t) <...
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作者：Weill, Mathilde
作者单位：Universite PSL; Ecole Normale Superieure (ENS)
摘要：In this work, we give a description of all a-finite measures on the space of rooted compact R-trees which satisfy a certain regenerative property. We show that any infinite measure which satisfies the regenerative property is the law of a Levy tree, that is, the law of a tree-valued random variable that describes the genealogy of a population evolving according to a continuous-state branching process. On the other hand, we prove that a probability measure with the regenerative property must be...
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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：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...
