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作者：Barton, NH; Etheridge, AM; Sturm, AK
作者单位：University of Edinburgh; University of Oxford; Technical University of Berlin
摘要：We consider a single genetic locus which carries two alleles, labelled P and Q. This locus experiences selection and mutation. It is linked to a second neutral locus with recombination rate r. If r = 0, this reduces to the study of a single selected locus. Assuming a Moran model for the population dynamics, we pass to a diffusion approximation and, assuming that the allele frequencies at the selected locus have reached stationarity, establish the joint generating function for the genealogy of ...
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作者：Neininger, R; Rüschendorf, L
作者单位：McGill University; University of Freiburg
摘要：Limit laws are proven by the contraction method for random vectors of a recursive nature as they arise as parameters of combinatorial structures such as random trees or recursive algorithms, where we use the Zolotarev metric. In comparison to previous applications of this method, a general transfer theorem is derived which allows us to establish a limit law on the basis of the recursive structure and the asymptotics of the first and second moments of the sequence. In particular, a general asym...
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作者：Chigansky, P; Liptser, R
作者单位：Tel Aviv University
摘要：The nonlinear filtering equation is said to be stable if it forgets the initial condition. It is known that the filter might be unstable even if the signal is an ergodic Markov chain. In general, the filtering stability requires stronger signal ergodicity provided by the, so called, mixing condition. The latter is formulated in terms of the transition probability density of the signal. The most restrictive requirement of the mixing condition is the uniform positiveness of this density. We show...
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作者：Boroczky, K; Reitzner, M
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; University of Freiburg
摘要：Choose n independent random points on the boundary of a convex body K subset of R-d. The intersection of the supporting halfspaces at these random points is a random convex polyhedron. The expectations of its volume, its surface area and its mean width are investigated. In the case that the boundary of K is sufficiently smooth, asymptotic expansions as n --> infinity are derived even in the case when the curvature is allowed to be zero. We compare our results to the analogous results for best ...
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作者：Cohort, P
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：We present some convergence results about the distortion D-mu,n,r(v) related to the Voronoi vector quantization of a mu-distributed random variable using n i.i.d. v-distributed codes. A weak law of large numbers for n(r/d)D(mu,n,r)(v) is derived essentially under a mu-integrability condition on a negative power of a delta-lower Radon-Nikodym derivative of v. Assuming in addition that the probability measure mu has a bounded epsilon-potential, we obtain a strong law of large numbers for n(r/d)D...
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作者：Janson, S; Tysk, J
作者单位：Uppsala University
摘要：We use a notion of stochastic time, here called volatility time, to show convexity of option prices in the underlying asset if the contract function is convex as well as continuity and monotonicity of the option price in the volatility. The volatility time is obtained as the almost surely unique stopping time solution to a random ordinary differential equation related to volatility. This enables us to write price processes, or processes modeled by local martingales, as Brownian motions with re...
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作者：Pergamenshchikov, S
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Rouen Normandie
摘要：The Leland strategy for an approximate hedging of the call option under transactions costs is studied. The rate of convergence in the Kabanov-Safarian theorem for the Leland strategy is found. The limit theorem for the hedging portfolio is proved.
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作者：Berkes, I; Horváth, J
作者单位：HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics; Hungarian Academy of Sciences; Utah System of Higher Education; University of Utah
摘要：For a LARCH (linear ARCH) sequence (Y-n, sigma(n),) exhibiting long range dependence, we determine the limiting distribution of sums Sigma f (y(n)), Sigma f (sigma(n)) for smooth functions f satisfying E(y(0)f' (y(0))) = 0, E (sigma(0)f' (sigma(0))) not equal 0. We also give an approximation formula for the above sums, providing the first term of the asymptotic expansions of Sigma f (y(n)), Sigma f (sigma(n)).
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作者：Chan, HP; Lai, TL
作者单位：National University of Singapore; Stanford University
摘要：Saddlepoint approximations are developed for Markov random walks S-n and are used to evaluate the probability that (j - i) g ((S-j - S-i) / (j - i)) exceeds a threshold value for certain sets of (i, j). The special case g(x) = x reduces to the usual scan statistic in change-point detection problems, and many generalized likelihood ratio detection schemes are also of this form with suitably chosen g. We make use of this boundary crossing probability to derive both the asymptotic Gumbel-type dis...
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作者：Cox, JT; Klenke, A
作者单位：Syracuse University; University of Cologne
摘要：Super Brownian motion is known to occur as the limit of properly rescaled interacting particle systems such as branching random walk, the contact process and the voter model. In this paper we show that certain linearly interacting diffusions converge to super Brownian motion if suitably rescaled in time and space. The results comprise nearest neighbor interaction as well as long range interaction.
