-
作者：Aldous, DJ; Bandyopadhyay, A
作者单位：University of California System; University of California Berkeley; University of Minnesota System; University of Minnesota Twin Cities
摘要：In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributional equation of the form X-d = g((xi(i), X-i), i >= 1). Here (xi(i)) and g((.)) are given and the X-i are independent copies of the unknown distribution X. We survey this area, emphasizing examples where the function g((.)) is essentially a maximum or minimum function. We draw attention to the theoretical...
-
作者：Bousquet-Mélou, M
作者单位：Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider planar lattice walks that start from (0, 0), remain in the first quadrant i, j >= 0, and are made of three types of steps: North-East, West and South. These walks are known to have remarkable enumerative and probabilistic properties: center dot they are counted by nice numbers [Kreweras, Cahiers du B.U.R.O 6 (1965) 5-105], center dot the generating function of these numbers is algebraic [Gessel, J. Statist. Plann. Inference 14 (1986) 49-58], center dot the stationary distribution o...
-
作者：Beskos, A; Roberts, GO
作者单位：Lancaster University
摘要：We describe a new, surprisingly simple algorithm, that simulates exact sample paths of a class of stochastic differential equations. It involves rejection sampling and, when applicable, returns the location of the path at a random collection of time instances. The path can then be completed without further reference to the dynamics of the target process.
-
作者：Becherer, D; Schweizer, M
作者单位：Imperial College London; Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We use probabilistic methods to study classical solutions for systems of interacting semilinear parabolic partial differential equations. In a modeling framework for a financial market with interacting Ito and point processes, such PDEs are shown to provide a natural description for the solution of hedging and valuation problems for contingent claims with a recursive payoff structure.
-
作者：Darling, RWR; Norris, JR
作者单位：University of Cambridge
摘要：The theme of this paper is the derivation of analytic formulae for certain large combinatorial structures. The formulae are obtained via fluid limits of pure jump-type Markov processes, established under simple conditions on the Laplace transforms of their Levy kernels. Furthermore, a related Gaussian approximation allows us to describe the randomness which may persist in the limit when certain parameters take critical values. Our method is quite general, but is applied here to vertex identifi...
-
作者：Hoffman, C
作者单位：University of Washington; University of Washington Seattle
摘要：We study a large family of competing spatial growth models. In these models the vertices in Z(d) can take on three possible states {0, 1, 2}. Vertices in states 1 and 2 remain in their states forever, while vertices in state 0, which are adjacent to a vertex in state 1 (or state 2), can switch to state 1 (or state 2). We think of the vertices in states 1 and 2 as infected with one of two infections, while the vertices in state 0 are considered uninfected. In this way these models are variants ...
-
作者：Kouritzin, MA; Sun, W
作者单位：University of Alberta; Concordia University - Canada
摘要：Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuous-discrete filtering problems. Suppose that t -> X-t is a Markov process and we wish to calculate the measure-valued process t -> mu(t) ((.)) = P{X-t is an element of (.)vertical bar sigma{Y-tk,Y- t(k) <= t}} where tk =k epsilon and Y-tk is a distorted, corrupted, partial observation of Xt(k). Then, one constructs a particle system with observation-dependent branching and n initial particl...
-
作者：Yan, LQ
作者单位：State University System of Florida; University of Florida
摘要：A Milstein-type scheme was proposed to improve the rate of convergence of its approximation of the solution to a stochastic differential equation driven by a vector of continuous semi martingales. A necessary and sufficient condition was provided for this rate to be 1/n when the SIDE is driven by a vector of continuous local martingales, or continuous semimartingales under an additional assumption on their finite variation part. The asymptotic behavior (weak convergence) of the normalized erro...
-
作者：Morrow, GJ; Zhang, Y
作者单位：University of Colorado System; University of Colorado at Colorado Springs
摘要：Let L-n denote the lowest crossing of a square 2n x 2n box for critical site percolation on the triangular lattice imbedded in Z(2). Denote also by F-n the pioneering sites extending below this crossing, and Q(n) the pivotal sites on this crossing. Combining the recent results of Smimov and Werner [Math. Res. Lett. 8 (2001) 729-744] on asymptotic probabilities of multiple arm paths in both the plane and half-plane, Kesten's [Comm. Math. Phys. 109 (1987) 109-156] method for showing that certain...
-
作者：Rasonyi, M; Stettner, L
作者单位：HUN-REN; HUN-REN Institute for Computer Science & Control; Hungarian Academy of Sciences; Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences
摘要：We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are constructed using optimal strategies.
