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作者：Rogers, LCG; Zane, O
作者单位：University of Bath
摘要：The use of saddlepoint approximations in statistics is a well-established technique for computing the distribution of a random variable whose moment generating function is known. In this paper, we apply the methodology to computing the prices of various European-style options, whose returns processes are not the Brownian motion with drift assumed in the Black-Scholes paradigm. Through a number of examples, we show that the methodology is generally accurate and fast.
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作者：Fleischmann, K; Klenke, A
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Erlangen Nuremberg
摘要：Given an (ordinary) super-Brownian motion (SBM) rho on R-d of dimension d = 2, 3, we consider a (catalytic) SBM X-rho on R-d with local branching rates rho(s)(dx). We show that X-t(rho) is absolutely continuous with a density function xi(t)(rho), say. Moreover, there exists a version of the map (t, z) --> xi(t)(rho)(z) which is l(infinity) and solves the heat equation off the catalyst rho; more precisely, off the (zero set of) closed support of the time-space measure ds rho(s)(dx). Using self-...
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作者：Coutin, L; Decreusefond, L
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; IMT - Institut Mines-Telecom; IMT Atlantique
摘要：We develop the filtering theory in the case where both the signal and the observation are solutions of some stochastic differential equation driven by a multidimensional fractional Brownian motion. We show that the classical approach fails to give a closed equation for the filter and we develop another approach using an auxiliary process-valued semimartingale which solves this problem theoretically.
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作者：Donnelly, P; Kurtz, TG
作者单位：University of Oxford; University of Wisconsin System; University of Wisconsin Madison
摘要：Infinite population genetic models with general type space incorporating mutation, selection and recombination are considered. The Fleming-Viot measure-valued diffusion is represented in terms of a countably infinite-dimensional process. The complete genealogy of the population at each time can be recovered from the model. Results are given concerning the existence of stationary distributions and ergodicity and absolute continuity of the stationary distribution for a model vith selection with ...
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作者：Häggström, O
作者单位：Chalmers University of Technology
摘要：The fuzzy Potts model arises by taking the q-state Potts model, then identifying r of the Potts spins with the fuzzy spin 0, and the remaining q - r Potts spins with the fuzzy spin 1. Here we extend a result of Chayes by showing that the fuzzy Potts model has positive correlations. We also give an application to the percolation-theoretic behavior of the Potts model on Z(2).
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作者：Capinski, M; Cutland, NJ
作者单位：University of Hull
摘要：Existence of solutions for stochastic Euler equations is proved for the two-dimensional case. The laws of solutions of stochastic Navier-Stokes equations are shown to be relatively compact and all limit points las the viscosity converges to zero) are laws of solutions to stochastic Euler equations.
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作者：Griffiths, RC; Tavaré, S
作者单位：University of Oxford; University of Southern California
摘要：Under the infinitely many sites mutation model, the mutational history of a sample of DNA sequences can be described by a unique gene tree. We show how to find the conditional distribution of the ages of the mutations and the time to the most recent common ancestor of the sample, given this gene tree. Explicit expressions for such distributions seem impossible to find for the sample sizes of interest in practice. We resort to a Monte Carlo method to approximate these distributions. We use this...
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作者：Bhattacharya, R
作者单位：Indiana University System; Indiana University Bloomington
摘要：Consider diffusions on R-k, k > 1, governed by the It (o) over cap equation dX(t) = {b(X(t)) + beta(X(t)/a)} dt + sigma dB(t), where b, beta are periodic with the same period and are divergence free, cr is nonsingular and a is a large integer. Two distinct Gaussian phases occur as time progresses. The initial phase is exhibited over times 1 much less than t much less than a(2/3). Under a geometric condition on the velocity field beta, the final Gaussian phase occurs for times t much greater th...
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作者：Milstein, GN; Tretyakov, MV
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; Ural Federal University
摘要：Mean-square approximations, which ensure boundedness of both time and space increments, are constructed for stochastic differential equations in a bounded domain. The proposed algorithms are based on a space-time discretization using a random walk over boundaries of small space-time parallelepipeds. To realize the algorithms, exact distributions for exit points of the space-time Brownian motion from a space-time parallelepiped are given. Convergence theorems are stated for the proposed algorit...
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作者：Cox, JT; Schinazi, RB
作者单位：Syracuse University; University of Colorado System; University of Colorado at Colorado Springs
摘要：We consider a gene with two alleles. Allele A is normal, allele S is abnormal. Individuals with genotype SS have a severe disease called sickle-cell disease. Individuals with genotype AS are not sick, and it is thought that they are more resistant to malarial infection than individuals with genotype AA. This could explain why the allele S has persisted in regions where malaria is endemic. We use a stochastic spatial process to test this hypothesis. For our model, we show that if the genotype A...
