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作者：Jentzen, Arnulf; Kloeden, Peter; Winkel, Georg
作者单位：Princeton University; Goethe University Frankfurt
摘要：Recently, in a paper by Jentzen and Kloeden [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 465 (2009) 649-667], a new method for simulating nearly linear stochastic partial differential equations (SPDEs) with additive noise has been introduced. The key idea was to use suitable linear functionals of the noise process in the numerical scheme which allow a higher approximation order to be obtained. Following this approach, a new simplified version of the scheme in the above named reference is ...
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作者：Guo, Xianping; Song, Xinyuan
作者单位：Sun Yat Sen University; Chinese University of Hong Kong
摘要：This paper is devoted to studying constrained continuous-time Markov decision processes (MDPs) in the class of randomized policies depending on state histories. The transition rates may be unbounded, the reward and costs are admitted to be unbounded from above and from below, and the state and action spaces are Polish spaces. The optimality criterion to be maximized is the expected discounted rewards, and the constraints can be imposed on the expected discounted costs. First, we give condition...
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作者：Hu, Yaozhong; Nualart, David; Song, Xiaoming
作者单位：University of Kansas
摘要：In this paper we study backward stochastic differential equations with general terminal value and general random generator. In particular, we do not require the terminal value be given by a forward diffusion equation. The randomness of the generator does not need to be from a forward equation, either. Motivated from applications to numerical simulations, first we obtain the L(p)-Holder continuity of the solution. Then we construct several numerical approximation schemes for backward stochastic...
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作者：Fahim, Arash; Touzi, Nizar; Warin, Xavier
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Electricite de France (EDF)
摘要：We consider the probabilistic numerical scheme for fully nonlinear partial differential equations suggested in [Comm. Pure Appl. Math. 60 (2007) 1081-1110] and show that it can be introduced naturally as a combination of Monte Carlo and finite difference schemes without appealing to the theory of backward stochastic differential equations. Our first main result provides the convergence of the discrete-time approximation and derives a bound on the discretization error in terms of the time step....
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作者：Douc, Randal; Garivier, Aurelien; Moulines, Eric; Olsson, Jimmy
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom SudParis; IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Lund University
摘要：Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models. The aim of this paper is to provide a foundation of particle-based approximation of such distributions and to analyze, in a common unifying framework, different schemes producing such approximations. In this setting, general convergence results, including exponential deviation inequalities and cen...
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作者：Fernholz, Daniel; Karatzas, Ioannis
摘要：In an equity market model with Knightian uncertainty regarding the relative risk and covariance structure of its assets, we characterize in several ways the highest return relative to the market that can be achieved using nonanticipative investment rules over a given time horizon, and under any admissible configuration of model parameters that might materialize. One characterization is in terms of the smallest positive supersolution to a fully nonlinear parabolic partial differential equation ...
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作者：Durrett, Rick; Mayberry, John
作者单位：Duke University; University of the Pacific
摘要：The goal of cancer genome sequencing projects is to determine the genetic alterations that cause common cancers. Many malignancies arise during the clonal expansion of a benign tumor which motivates the study of recurrent selective sweeps in an exponentially growing population. To better understand this process, Beerenwinkel et al. [PLoS Comput. Biol. 3 (2007) 2239-2246] consider a Wright-Fisher model in which cells from an exponentially growing population accumulate advantageous mutations. Si...
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作者：Ichiba, Tomoyuki; Papathanakos, Vassilios; Banner, Adrian; Karatzas, Ioannis; Fernholz, Robert
作者单位：University of California System; University of California Santa Barbara
摘要：We study Atlas-type models of equity markets with local characteristics that depend on both name and rank, and in ways that induce a stable capital distribution. Ergodic properties and rankings of processes are examined with reference to the theory of reflected Brownian motions in polyhedral domains. In the context of such models we discuss properties of various investment strategies, including the so-called growth-optimal and universal portfolios.
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作者：Kaspi, Haya; Ramanan, Kavita
作者单位：Technion Israel Institute of Technology; Brown University
摘要：This work considers a many-server queueing system in which customers with independent and identically distributed service times, chosen from a general distribution, enter service in the order of arrival. The dynamics of the system are represented in terms of a process that describes the total number of customers in the system, as well as a measure-valued process that keeps track of the ages of customers in service. Under mild assumptions on the service time distribution, as the number of serve...
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作者：van den Berg, J.
作者单位：Centrum Wiskunde & Informatica (CWI); Vrije Universiteit Amsterdam
摘要：For ordinary (independent) percolation on a large class of lattices it is well known that below the critical percolation parameter pc the cluster size distribution has exponential decay and that power-law behavior of this distribution can only occur at pc. This behavior is often called sharpness of the percolation transition. For theoretical reasons, as well as motivated by applied research, there is an increasing interest in percolation models with (weak) dependencies. For instance, biologist...
