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作者：Pang, Huadong; Stroock, Daniel W.
作者单位：Massachusetts Institute of Technology (MIT)
摘要：In this paper we consider a one-dimensional diffusion equation on the interval [0, 1] satisfying non-Feller boundary conditions. As a consequence, the initial value Cauchy problem fails to preserve nonnegativity or boundedness. Nonetheless, probability theory plays an interesting role in our analysis and understanding of solutions to this equation.
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作者：Berti, Patrizia; Rigo, Pietro
作者单位：Universita di Modena e Reggio Emilia; University of Pavia
摘要：Let (ohm, B, P) be a probability space, A subset of B a sub-alpha-field, and mu a regular conditional distribution for P given A. Necessary and sufficient conditions for mu (w) (A) to be 0-1, for all A is an element of A and w is an element of A(0), where A(0) is an element of A and P(A(0)) = 1, are given. Such conditions apply, in particular, when A is a tail sub-alpha-field. Let H(w) denote the A-atom including the point w is an element of ohm. Necessary and sufficient conditions for mu(w) (...
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作者：Chalendar, Isabelle; Partington, Jonathan R.
作者单位：Universite Claude Bernard Lyon 1; University of Leeds
摘要：We prove a multivariable approximate Carleman theorem on the determination of complex measures on R-n and R-+(n) by their moments. This is achieved by means of a multivariable Denjoy-Carleman maximum principle for quasi-analytic functions of several variables. As an application, we obtain a discrete Phragmen-Lindelof-type theorem for analytic functions on C-+(n).
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作者：Pemantle, Robin; Peres, Yuval
作者单位：University of Pennsylvania; University of California System; University of California Berkeley
摘要：We give potential theoretic estimates for the probability that a set A contains a double point of planar Brownian motion run for unit time. Unlike the probability for A to intersect the range of a Markov process, this cannot be estimated by a capacity of the set A. Instead, we introduce the notion of a capacity with respect to two gauge functions simultaneously. We also give a polar decomposition of A into a set that never intersects the set of Brownian double points and a set for which inters...
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作者：Swanson, Jason
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：We consider the solution to a stochastic heat equation. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time, F(t), has a nontrivial quartic variation. This process, therefore, has infinite quadratic variation and is not a semimartingale. It follows that the classical Ito calculus does not apply. Motivated by heuristic ideas about a possible new calculus for this process, we are led to study modifications of the quadratic varia...
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作者：Bai, Z. D.; Miao, B. Q.; Pan, G. M.
作者单位：Northeast Normal University - China; Northeast Normal University - China; Chinese Academy of Sciences; University of Science & Technology of China, CAS; National University of Singapore
摘要：Let {X-ij}, i, j = .... be a double array of i.i.d. complex random variables with EX11 =0, E vertical bar X-11 vertical bar(2) = 1 and E vertical bar X-11 vertical bar(4) < infinity, and let A(n) = 1/N T-n(1/2) X-n (XnTn1/2)-T-*, where T-n(1/2) is the square root of a nonnegative definite matrix T-n and X-n is the n x N matrix of the upper-left corner of the double array. The matrix A(n) can be considered as a sample covariance matrix of an i.i.d. sample from a population with mean zero and co...
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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...
