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作者：Fusai, G
作者单位：University of Florence
摘要：We study a generalization of the are-sine law In particular we provide new results about the distribution of the time spent by a BM with drift inside a band, giving the Laplace transform of the characteristic function. If one of the extremes of the band goes to infinity, our formula agrees with the results given in Akahori and Takacs. We apply these results to the pricing of exotic option contracts known as corridor derivatives. We then discuss the inversion problem comparing different numeric...
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作者：Burdzy, K; Kendall, WS
作者单位：University of Washington; University of Washington Seattle; University of Warwick
摘要：In this paper we study the notion of an efficient coupling of Markov processes. Informally, an efficient coupling is one which couples at the maximum possible exponential rate, as given by the spectral gap. This notion is of interest not only for its own sake, but also of growing importance arising from the recent advent of methods of perfect simulation: it helps to establish the price of perfection for such methods. In general, one can always achieve efficient coupling if the coupling is allo...
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作者：Hofmann, N; Müller-Gronbach, T; Ritter, K
作者单位：University of Passau; Free University of Berlin; University of Erlangen Nuremberg
摘要：We analyze the pathwise approximation for systems of stochastic differential equations. The pathwise distance between the solution and its approximation is measured globally on the unit interval in the L-infinity-norm, and we study the expectation of this distance. For systems with additive noise we obtain sharp lower and upper bounds for the minimal error in the class of arbitrary methods which use discrete observations of a Brownian path. The optimal order is achieved by an Euler scheme with...
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作者：Evans, W; Kenyon, C; Peres, Y; Schulman, LJ
作者单位：University of Arizona; Universite Paris Saclay; University of California System; University of California Berkeley; Hebrew University of Jerusalem; University System of Georgia; Georgia Institute of Technology
摘要：Consider a process in which information is transmitted from a given root node on a noisy tree network T. We start with an unbiased random bit R at the root of the tree and send it down the edges of T. On every edge the bit can be reversed with probability epsilon, and these errors occur independently. The goal is to reconstruct R from the values which arrive at the nth level of the tree. This model has been studied in information theory, genetics and statistical mechanics. We bound the reconst...
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作者：Arratia, R; Barbour, AD; Tavaré, S
作者单位：University of Southern California; University of Zurich
摘要：Under very mild conditions, we prove that the number of components in a decomposable logarithmic combinatorial structure has a distribution which is close to Poisson in total variation. The conditions are satisfied for all assemblies, multisets and selections in the logarithmic class. The error in the Poisson approximation is shown under marginally more restrictive conditions to be of exact order O(1/ log n), by exhibiting the penultimate asymptotic approximation; similar results have previous...
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作者：Penrose, MD
作者单位：Durham University
摘要：Given an ordering of the vertices of a finite graph, let the induced weight for an edge be the separation of its endpoints in the ordering. Layout problems involve choosing the ordering to minimize a cost functional such as the sum or maximum of the edge weights. We give growth rates for the costs of some of these problems on supercritical percolation processes and supercritical random geometric graphs, obtained by placing vertices randomly in the unit cube and joining them whenever at most so...
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作者：Yin, G; Zhang, Q; Badowski, G
作者单位：Wayne State University; University System of Georgia; University of Georgia
摘要：This work is concerned with aggregations in a singularly perturbed Markov chain having a finite state space and fast and slow motions. The state space of the underlying Markov chain can be decomposed into several groups of recurrent states and a group of transient states. The asymptotic properties are studied through sequences of unscaled and scaled occupation measures. By treating the states within each recurrent class as a single state, an aggregated process is defined and shown to be conver...
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作者：Erhardsson, T
作者单位：Royal Institute of Technology
摘要：We consider the number of overlapping occurrences up to a fixed time of one or several rare patterns in a stationary finite-state Markov chain. We derive a bound for the total variation distance between the distribution of this quantity and a compound Poisson distribution, using general results on compound Poisson approximation for Markov chains by Erhardsson. If the state space is {0, 1} and the pattern is a head run (111...111), the bound is completely explicit and improves on an earlier bou...
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作者：Mykland, PA
作者单位：University of Chicago
摘要：It is common to have interval predictions for volatilities and other quantities governing securities prices. The purpose of this paper is to provide an exact method for converting such intervals into arbitrage based prices of financial derivatives or industrial or contractual options. We call this procedure conservative delta hedging. The proposed approach will permit an institution's management a greater oversight of its exposure to risk.
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作者：Mézières, S; Roynette, B
作者单位：Universite de Lorraine
摘要：This paper is concerned with the simulation of a a-dimensional stochastic differential equation motivated by some physical phenomena of fluid mechanics. The drift and diffusion coefficients of the equation admitting local singularities, we are led to study a particular term of strong perturbation denoted by Brownian impulse. Our suggestion for the simulation is to replace the singularity by a jump on which our study therefore focuses.
