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作者：Yukich, J. E.
作者单位：Lehigh University
摘要：Let P lambda := P lambda kappa denote a Poisson point process of intensity lambda kappa on [0,1](d), d >= 2, with K a bounded density on [0,1](d) and A e (0, co). Given a closed subset M c [0, lid of Hausdorff dimension (d 1), we consider general statistics E 7,2, (x, PA, M), where the score function 4 vanishes unless the input x is close to M and where satisfies a weak spatial dependency condition. We give a rate of normal convergence for the rescaled statistics ExEPA. (X x ' lld Al/divt. as ...
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作者：Hernandez-Hernandez, Daniel; Simon, Robert S.; Zervos, Mihail
作者单位：CIMAT - Centro de Investigacion en Matematicas; University of London; London School Economics & Political Science
摘要：We consider a stochastic differential equation that is controlled by means of an additive finite-variation process. A singular stochastic controller, who is a minimizer, determines this finite-variation process, while a discretionary stopper, who is a maximizer, chooses a stopping time at which the game terminates. We consider two closely related games that are differentiated by whether the controller or the stopper has a first-move advantage. The games' performance indices involve a running p...
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作者：Shaikhet, Gennady
作者单位：Carleton University
摘要：Throughput sub-optimality (TSO), introduced in Atar and Shaikhet [Ann. AppL Probab. 19 (2009) 521-555] for static fluid models of parallel queueing networks, corresponds to the existence of a resource allocation, under which the total service rate becomes greater than the total arrival rate. As shown in Atar, Mandelbaum and Shaikhet [Ann. AppL Probab. 16 (2006) 1764-1804] and Atar and Shaikhet (2009), in the many server Halfin Whitt regime, TSO implies null controllability (NC), the existence ...
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作者：Ben Alaya, Mohamed; Kebaier, Armed
作者单位：Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：This paper focuses on studying the multilevel Monte Carlo method recently introduced by Giles [Oper. Res. 56 (2008) 607-617] which is significantly more efficient than the classical Monte Carlo one. Our aim is to prove a central limit theorem of Lindeberg Feller type for the multilevel Monte Carlo method associated with the Euler discretization scheme. To do so, we prove first a stable law convergence theorem, in the spirit of Jacod and Protter [Ann. Probab. 26 (1998) 267-307], for the Euler s...
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作者：Lorig, Matthew; Pagliarani, Stefano; Pascucci, Andrea
作者单位：Princeton University; Institut Polytechnique de Paris; Ecole Polytechnique; University of Bologna
摘要：We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Levy-type martingale subject to default. This class of models allows for local volatility, local default intensity and a locally dependent Levy measure. Generalizing and extending the novel adjoint expansion technique of Pagliarani, Pascucci and Riga [SIAM J. Financial Math. 4 (2013) 265-296], we derive a family of asymptotic expansions for the transition density of the underlying as well as for...
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作者：Andrieu, Christophe; Tadic, Vladislav B.; Vihola, Matti
作者单位：University of Bristol; University of Jyvaskyla
摘要：We develop a practical approach to establish the stability, that is, the recurrence in a given set, of a large class of controlled Markov chains. These processes arise in various areas of applied science and encompass important numerical methods. We show in particular how individual Lyapunov functions and associated drift conditions for the parametrized family of Markov transition probabilities and the parameter update can be combined to form Lyapunov functions for the joint process, leading t...
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作者：Auffinger, Antonio; Damron, Michael; Hanson, Jack
作者单位：University of Chicago; Indiana University System; Indiana University Bloomington
摘要：It is an open problem to show that in two-dimensional first-passage percolation, the sequence of finite geodesics from any point to (n, 0) has a limit in n. In this paper, we consider this question for first-passage percolation on a wide class of subgraphs of Z(2): those whose vertex set is infinite and connected with an infinite connected complement. This includes, for instance, slit planes, half-planes and sectors. Writing x(n) for the sequence of boundary vertices, we show that the sequence...
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作者：Lachieze-Rey, Raphael; Molchanov, Ilya
作者单位：Universite Paris Cite; University of Bern
摘要：We study existence of random elements with partially specified distributions. The technique relies on the existence of a positive extension for linear functionals accompanied by additional conditions that ensure the regularity of the extension needed for interpreting it as a probability measure. It is shown in which case the extension can be chosen to possess some invariance properties. The results are applied to the existence of point processes with given correlation measure and random closed...
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作者：Ferrari, Giorgio
作者单位：University of Bielefeld
摘要：In this paper, we derive a new handy integral equation for the freeboundary of infinite time horizon, continuous time, stochastic, irreversible investment problems with uncertainty modeled as a one-dimensional, regular diffusion X. The new integral equation allows to explicitly find the freeboundary b(.) in some so far unsolved cases, as when the operating profit function is not multiplicatively separable and X is a three-dimensional Bessel process or a CEV process. Our result follows from pur...
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作者：Mueller, Sebastian
作者单位：Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：The aim of this paper is to undetline the relation between reversible growth processes and invariant percolation. We present two models of interacting branching random walks (BRWs), truncated BRWs and competing BRWs, where survival of the growth process can be formulated as the existence of an infinite cluster in an invariant percolation on a tree. Our approach is fairly conceptual and allows generalizations to a wider set of reversible growth processes.
