2期

最新文章

• The optimal uniform approximation of systems of stochastic differential equations AI翻译
  作者：Müller-Gronbach, T
  作者单位：Technical University of Darmstadt
  摘要：We analyze numerical methods for the pathwise approximation of a system of stochastic differential equations. As a measure of performance we consider the qth mean of the maximum distance between the solution and its approximation on the whole unit interval. We introduce an adaptive discretization that takes into account the local smoothness of every trajectory of the solution. The resulting adaptive Euler approximation performs asymptotically optimal in the class of all numerical methods that ...
• Clusters and recurrence in the two-dimensional zero-temperature stochastic Ising model AI翻译
  作者：Camia, F; De Santis, E; Newman, CM
  作者单位：New York University; Sapienza University Rome; New York University
  摘要：We analyze clustering and (local) recurrence of a standard Markov process model of spatial domain coarsening. The continuous time process, whose state space consists of assignments of +1 or -1 to each site in Z(2), is the zero-temperature limit of the stochastic homogeneous Ising ferromagnet (with Glauber dynamics): the initial state is chosen uniformly at random and then each site, at rate 1, polls its four neighbors and makes sure it agrees with the majority, or tosses a fair coin in case of...
• The shape theorem for the frog model AI翻译
  作者：Alves, OSM; Machado, FP; Popov, SY
  作者单位：Universidade de Sao Paulo
  摘要：We prove a shape theorem for a growing set of simple random walks on Z(d), known as the frog model. The dynamics of this process is described as follows: There are active particles, which perform independent discrete time SRWs, and sleeping particles, which do not move. When a sleeping particle is hit by an active particle, it becomes active too. At time 0 all particles are sleeping, except for that placed at the origin. We prove that the set of the original positions of all active particles, ...
• Eternal solutions to Smoluchowski's coagulation equation with additive kernel and their probabilistic interpretations AI翻译
  作者：Bertoin, J
  作者单位：Universite Paris Cite; Sorbonne Universite; Institut Universitaire de France; Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
  摘要：The cornerstone of this work, which is partly motivated by the characterization of the so-called eternal additive coalescents by Aldous and Pitman, is an explicit expression for the general eternal solution to Smoluchowski's coagulation equation with additive kernel. This expression points at certain Levy processes with no negative jumps and more precisely at a stochastic model for aggregation based on such processes, which has been recently considered by Bertoin and Miermont and is known to b...
• Risk-sensitive control and an optimal investment model II AI翻译
  作者：Fleming, WH; Sheu, SJ
  作者单位：Brown University; Academia Sinica - Taiwan
  摘要：We consider an optimal investment problem proposed by Bielecki and Pliska. The goal of the investment problem is to optimize the long-term growth of expected utility of wealth. We consider HARA utility functions with exponent -infinity < gamma < 1. The problem can be reformulated as an infinite time horizon risk-sensitive control problem. Some useful ideas and results from the theory of risk-sensitive control can be used in the analysis. Especially, we analyze the associated dynamical programm...
• Rate of convergence of a particle method to the solution of the McKean-Vlasov equation AI翻译
  作者：Antonelli, F; Kohatsu-Higa, A
  作者单位：G d'Annunzio University of Chieti-Pescara; Pompeu Fabra University; Purdue University System; Purdue University
  摘要：This paper studies the rate of convergence of an appropriate discretization scheme of the solution of the McKean-Vlasov equation introduced by Bossy and Talay. More specifically, we consider approximations of the distribution and of the density of the solution of the stochastic differential equation associated to the McKean-Vlasov equation. The scheme adopted here is a mixed one: Euler-weakly interacting particle system. If n is the number of weakly interacting particles and h is the uniform s...
• Approximate Ewens formulae for symmetric overdominance selection AI翻译
  作者：Grote, MN; Speed, TP
  作者单位：University of California System; University of California Davis; University of California System; University of California Berkeley
  摘要：We derive a family of approximate sampling distributions for the symmetric overdominance model of population genetics. The distributions are selective versions of the Ewens Sampling Formula, which gives sample likelihoods under a model of neutral evolution. We draw on basic results for the general selection model of Ethier and Kurtz, and use mathematical tools well-suited for calculating expectations of symmetric functions of Poisson-Dirichlet atoms. We conclude by briefly examining a Human Le...
• Markovian term structure models in discrete time AI翻译
  作者：Filipovic, D; Zabczyk, J
  作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; Polish Academy of Sciences
  摘要：In this article we discuss Markovian term structure models in discrete time and with continuous state space. More precisely, we are concerned with the structural properties of such models if one has the Markov property for a part of the forward curve. We investigate the two cases where these parts are either a true subset of the forward curve, including the short rate, or the entire forward curve. For the former case we give a sufficient condition for the term structure model to be affine. For...
• Bins and balls: Large deviations of the empirical occupancy process AI翻译
  作者：Boucheron, S; Gamboa, F; Léonard, C
  作者单位：Universite Paris Saclay; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Paris Nanterre
  摘要：In the random allocation model, balls are sequentially inserted at random into n exchangeable bins. The occupancy score of a bin denotes the number of balls inserted in this bin. The (random) distribution of occupancy scores defines the object of this paper: the empirical occupancy measure which is a probability measure over the integers. This measure-valued random variable packages many useful statistics. This paper characterizes the large deviations of the flow of empirical occupancy measure...
• Utility based optimal hedging in incomplete markets AI翻译
  作者：Owen, MP
  作者单位：Technische Universitat Wien
  摘要：We provide the solution to a fusion of two fundamental problems in mathematical finance. The first problem is that of maximizing the expected utility of terminal wealth of an investor who holds a short position in a contingent claim, and the second is that of maximizing terminal wealth where the utility function allows the investor to have negative wealth. Under assumptions of reasonable asymptotic elasticity on the investor's utility function, we present an optimal investment theorem and simu...