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作者：CHEN, LHY; ROOS, M
作者单位：University of Zurich
摘要：A second order error bound is obtained for approximating integral h d (Q) over tilde by integral h dQ, where (Q) over tilde is a convolution of measures and Q a compound Poisson measure on a measurable abelian group, and the function h is not necessarily bounded. This error bound is more refined than the usual total variation bound in the sense that it contains the function h. The method used is inspired by Stein's method and hinges on bounding Radon-Nikodym derivatives related to d (Q) over t...
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作者：GYONGY, I; NUALART, D; SANZSOLE, M
作者单位：University of Barcelona
摘要：We prove an approximation theorem for stochastic differential equations, under rather weak smoothness conditions on the coefficients, when the driving semimartingales are approximated by continuous semimartingales, in probability, and the solutions are considered in several Banach spaces, defined in terms of different types of the modulus of continuity. Hence Stroock-Varadhan's support theorem is obtained in these spaces, in particular, in appropriate Besov and Holder spaces.
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作者：BERTOIN, J
摘要：Let G = (G(t), t greater than or equal to 0) be the process of last passage times at some fixed point of a Markov process. The Dynkin-Lamperti theorem provides a necessary and sufficient condition for G(t)/t to converge in law as t --> infinity to some non-degenerate limit (which is then a generalized arcsine law). Under this condition, we give a simple integral test that characterizes the lower-functions of G. We obtain a similar result for A(+) = (A(+)(t),t greater than or equal to 0), the t...
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作者：HU, Y; SHI, Z
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：Let {W(t); 0 less than or equal to t less than or equal to 1} be a two-dimensional Wiener process starting from 0. We are interested in the almost sure asymptotic behaviour, as r tends to 0, of the processes X(r) and Y(r), where X(r) denotes the total time spent by W in the ball centered at 0 with radius r, and Y(r) the distance between 0 and the curve (W(t); r less than or equal to t less than or equal to 1}. While a characterization of the lower functions of Y was previously established by S...
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作者：BASS, RF; BURDZY, K
摘要：We give an upper bound for the Green functions of conditioned Brownian motion in planar domains. A corollary is the conditional gauge theorem in bounded planar domains.
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作者：MATHIEU, P
摘要：We prove L(p) majorations for the suprema of the intersection local time of two planar Brownian motions. We deduce a sufficient condition on the correlation of two Brownian motions for their i.l.t. to be continuous.
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作者：COFFMAN, EG; POONEN, B; WINKLER, P
作者单位：Nokia Corporation; Nokia Bell Labs; AT&T
摘要：Let n random intervals I-1,...,I-n be chosen by selecting endpoints independently from the uniform distribution on [0,1]. A packing is a pairwise disjoint subset of the intervals; its wasted space is the Lebesgue measure of the points of [0,1] not covered by the packing. In any set of intervals the packing with least wasted space is computationally easy to find; but its expected wasted space in the random case is not obvious. We show that with high probability for large n, this ''best'' packin...
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作者：GRAHAM, C
摘要：We study a process reflecting in a domain. The process follows Wentzell non-sticky boundary conditions while being adsorbed at the boundary at a certain rate with respect to local time and desorbed at a rate with respect to natural time. We show that when the rates go to infinity with a converging ratio, the process converges to a process with sticky reflection having the limit ratio as the sojourn coefficient. We then study a mean-field interacting system of such particles. We show propagatio...
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作者：MYKLAND, PA
摘要：The paper develops a way of embedding general martingales in continuous ones in such a way that the quadratic variation of the continuous martingale has conditional cumulants (given the original martingale) that are explicitly given in terms of optional and predictable variations of the original process. Bartlett identities for the conditional cumulants are also found. A main corollary to these results is the establishment of second (and in some cases higher) order asymptotic expansions for ma...
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作者：COX, JT; GREVEN, A; SHIGA, T
作者单位：University of Erlangen Nuremberg; Institute of Science Tokyo; Tokyo Institute of Technology
摘要：We study the problem of relating the long time behavior of finite and infinite systems of locally interacting components. We consider in detail a class of linearly interacting diffusions x(t) = {x(i)(t), i is an element of Z(d)}, in the regime where there is a one-parameter family of nontrivial invariant measures. For these systems there are naturally defined corresponding finite systems, x(N)(t) = {x(i)(N)(t), i is an element of Lambda(N)}, with Lambda(N) = (-N,N](d) boolean AND Z(d). Our mai...
