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作者：Sezer, Deniz
作者单位：York University - Canada
摘要：We develop the mathematics of a filtration shrinkage model that has recently been considered in the credit risk modeling literature. Given a finite collection of points x(1) < ... < x(N) in R, the region indicator function R(x) assumes the value i if x is an element of (x(i - 1), x(i)]. We take F to be the filtration generated by (R(X-t))(t >= 0), where X is a diffusion with infinitesimal generator A. We prove a martingale representation theorem for F in terms of stochastic integrals with resp...
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作者：Coviello, Rosanna; Russo, Francesco
作者单位：Scuola Normale Superiore di Pisa; Universite Paris 13
摘要：In this paper we discuss existence and uniqueness for a one-dimensional time inhomogeneous stochastic differential equation directed by an F-semi-martingale M and a finite cubic variation process which has the structure Q + R, where Q is a finite quadratic variation process and R is strongly predictable in some technical sense: that condition implies, in particular, that R is weak Dirichlet, and it is fulfilled, for instance, when R is independent of M. The method is based on a transformation ...
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作者：Brydges, David; van der Hofstad, Remco; Koenig, Wolfgang
作者单位：University of British Columbia; Eindhoven University of Technology; Leipzig University
摘要：We investigate the local times of a continuous-time Markov chain on an arbitrary discrete state space. For fixed finite range of the Markov chain, we derive an explicit formula for the joint density of all local times on the range, at any fixed time. We use standard tools from the theory of stochastic processes and finite-dimensional complex calculus. We apply this formula in the following directions: (1) we derive large deviation upper estimates for the normalized local times beyond the expon...
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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：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...
