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作者：van Enter, Aernout C. D.; Kulske, Christof
作者单位：University of Groningen
摘要：We consider statistical mechanics models of continuous spins in a disordered environment. These models have a natural interpretation as effective interface models. It is well known that without disorder there are no interface Gibbs measures in infinite volume in dimension d = 2, while there are gradient Gibbs measures describing an infinite-volume distribution for the increments of the field, as was shown by Funaki and Spohn. In the present paper we show that adding a disorder term prohibits t...
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作者：Barbour, A. D.; Luczak, M. J.
作者单位：University of Zurich; University of London; London School Economics & Political Science
摘要：In modeling parasitic diseases, it is natural to distinguish hosts according to the number of parasites that they carry, leading to a countably infinite type space. Proving the analogue of the deterministic equations, used in models with finitely many types as a law of large numbers approximation to the underlying stochastic model, has previously either been done case by case, using some special structure, or else not attempted. In this paper we prove a general theorem of this sort, and comple...
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作者：Budhiraja, Amarjit; Ross, Kevin
作者单位：University of North Carolina; University of North Carolina Chapel Hill; Stanford University
摘要：A singular stochastic control problem with state constraints in two-dimensions is studied. We show that the value function is C(1) and its directional derivatives are the value functions of certain optimal stopping problems. Guided by the optimal stopping problem, we then introduce the associated no-action region and the free boundary and show that, under appropriate conditions, an optimally controlled process is a Brownian motion in the no-action region with reflection at the free boundary. T...
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作者：Loeffen, R. L.
作者单位：University of Bath
摘要：We consider the classical optimal dividend control problem which was proposed by de Finetti [Trans. XVth Internat. Congress Actuaries 2 (1957) 433-443]. Recently Avram, Palmowski and Pistorius [Ann. Appl. Probab. 17 (2007) 156-180] studied the case when the risk process is modeled by a general spectrally negative Levy process. We draw upon their results and give sufficient conditions under which the optimal strategy is of barrier type, thereby helping to explain the fact that this particular s...
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作者：Rueschendorf, Ludger; Urusov, Mikhail A.
作者单位：University of Freiburg; Technical University of Berlin; Deutsche Bank
摘要：In this paper, we introduce a modification of the free boundary problem related to optimal stopping problems for diffusion processes. This modification allows the application of this PDE method in cases where the usual regularity assumptions on the coefficients and on the gain function are not satisfied. We apply this method to the optimal stopping of integral functionals with exponential discount of the form E-x root(tau)(0)e-(lambda s) f (X-s) ds, lambda >= 0 for one-dimensional diffusions X...
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作者：Mora, Carlos M.; Rebolledo, Rolando
作者单位：Universidad de Concepcion; Universidad de Concepcion; Pontificia Universidad Catolica de Chile
摘要：The paper is devoted to the study of nonlinear stochastic Schrodinger equations driven by standard cylindrical Brownian motions (NSSEs) arising from the unraveling of quantum master equations. Under the Born-Markov approximations, this class of stochastic evolutions equations on Hilbert spaces provides characterizations of both continuous quantum measurement processes and the evolution of quantum systems. First, we deal with the existence and uniqueness of regular solutions to NSSEs. Second, w...
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作者：Debussche, Arnaud; Gautier, Eric
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider the problem of the error in soliton transmission in long-haul optical fibers caused by the spontaneous emission of noise inherent to amplification. We study two types of noises driving the stochastic focusing cubic one dimensional nonlinear Schrodinger equation which appears in physics in that context. We focus on the fluctuations of the mass and arrival time or timing jitter. We give the small noise asymptotic of the tails of these two quantities for the two types of noises. We ar...
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作者：Fort, Gersende; Meyn, Sean; Moulines, Eric; Priouret, Pierre
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Centre National de la Recherche Scientifique (CNRS); University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign; Sorbonne Universite; Universite Paris Cite
摘要：In this paper, some of these techniques are extended to a general class of skip-free Markov chains. As in the case of queueing models, a fluid approximation is obtained by scaling time, space and the initial condition by a large constant. The resulting fluid limit is the solution of an ordinary differential equation (ODE) in most of the state space. Stability and finer ergodic properties for the stochastic model then follow from stability of the set of fluid limits. Moreover, similarly to the ...
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作者：Jourdain, Benjamin; Malrieu, Florent
作者单位：Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Universite de Rennes
摘要：In this paper, in the particular case of a concave flux function, we are interested in the long time behavior of the nonlinear process associated in [Methodol. Comput. Appl. Probab. 2 (2000) 69-91] to the one-dimensional viscous scalar conservation law. We also consider the particle system obtained by replacing the cumulative distribution function in the drift coefficient of this nonlinear process by the empirical cumulative distribution function. We first obtain a trajectorial propagation of ...
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作者：Austin, Tim D.
作者单位：University of California System; University of California Los Angeles
摘要：In this paper we consider the classical differential equations of Hodgkin and Huxley and a natural refinement of them to include a layer of stochastic behavior, modeled by a large number of finite-state-space Markov processes coupled to a simple modification of the original Hodgkin-Huxley PDE. We first prove existence, uniqueness and some regularity for the stochastic process, and then show that in a suitable limit as the number of stochastic components of the stochastic model increases and th...
