1999

最新文章

• Stochastic calculus for Brownian motion on a Brownian fracture AI翻译
  作者：Khoshnevisan, D; Lewis, TM
  作者单位：Utah System of Higher Education; University of Utah
  摘要：In this paper, we give a pathwise development of stochastic integrals with respect to iterated Brownian motion. We also provide a detailed analysis of the variations of iterated Brownian motion. These variations are linked to Brownian motion in random scenery and iterated Brownian motion itself.
• The asymptotic elasticity of utility functions and optimal investment in incomplete markets AI翻译
  作者：Kramkov, D; Schachermayer, W
  作者单位：Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; Technische Universitat Wien; University of Vienna
  摘要：The paper studies the problem of maximizing the expected utility of terminal wealth in the framework of a general incomplete semimartingale model of a financial market. We show that the necessary and sufficient condition on a utility function for the validity of several key assertions of the theory to hold true is the requirement that the asymptotic elasticity of the utility function is strictly less than 1.
• A remark on random perturbations of the nonlinear pendulum AI翻译
  作者：Freidlin, M; Weber, M
  作者单位：University System of Maryland; University of Maryland College Park; Technische Universitat Dresden
  摘要：We describe the long-time behavior of the nonlinear pendulum perturbed by a small noise. To derive this asymptotics, one has to consider diffusion processes on the graph corresponding to the Hamiltonian of the pendulum.
• Saddlepoint approximations to option prices AI翻译
  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.
• Smooth density field of catalytic super-Brownian motion AI翻译
  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-...
• Abstract nonlinear filtering theory in the presence of fractional Brownian motion AI翻译
  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.
• Genealogical processes for Fleming-Viot models with selection and recombination AI翻译
  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 ...
• Positive correlations in the fuzzy Potts model AI翻译
  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).
• Stochastic Euler equations on the torus AI翻译
  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.
• The ages of mutations in gene trees AI翻译
  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...