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作者：Fromm, Alexander; Imkeller, Peter
作者单位：Friedrich Schiller University of Jena; Humboldt University of Berlin
摘要：We consider the utility maximization problem for a general class of utility functions defined on the real line. We rely on existing results which reduce the problem to a coupled forward-backward stochastic differential equation (FBSDE) and concentrate on showing existence and uniqueness of solution processes to this FBSDE. We use the method of decoupling fields for strongly coupled, multi-dimensional and possibly non-Lipschitz systems as the central technique in conducting the proofs.
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作者：Bank, Peter; Besslich, David
作者单位：Technical University of Berlin
摘要：In stochastic control problems delicate issues arise when the controlled system can jump due to both exogenous shocks and endogenous controls. Here one has to specify what the controller knows when about the exogenous shocks and how and when she can act on this information. We propose to use Meyer-sigma-fields as a flexible tool to model information flow in such situations. The possibilities of this approach are illustrated first in a very simple linear stochastic control problem and then in a...
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作者：Buijsrogge, Anne; Dupuis, Paul; Snarski, Michael
作者单位：University of Twente; Brown University
摘要：In this paper we study the performance of splitting algorithms, and in particular the RESTART method, for the numerical approximation of the probability that a process leaves a neighborhood of a metastable point during some long time interval [0, T]. We show that, in contrast to alternatives such as importance sampling, the decay rate of the second moment does not degrade as T -> infinity. In the course of the analysis we develop some related large deviation estimates that apply when the time ...
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作者：Harris, Simon C.; Horton, Emma; Kyprianou, Andreas E.
作者单位：University of Auckland; Universite de Lorraine; University of Bath
摘要：The neutron transport equation (NTE) describes the flux of neutrons across a planar cross-section in an inhomogeneous fissile medium when the process of nuclear fission is active. Classical work on the NTE emerges from the applied mathematics literature in the 1950s through the work of R. Dautray and collaborators (Methodes Probabilistes Pour les equations de la Physique (1989) Eyrolles; Mathematical Analysis and Numerical Methods for Science and Technology. Vol. 6: Evolution Problems. II (199...
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作者：Peres, Yuval; Racz, Miklos Z.; Sly, Allan; Stuhl, Izabella
作者单位：Princeton University; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：It is well known that sequential decision making may lead to information cascades. That is, when agents make decisions based on their private information, as well as observing the actions of those before them, then it might be rational to ignore their private signal and imitate the action of previous individuals. If the individuals are choosing between a right and a wrong state, and the initial actions are wrong, then the whole cascade will be wrong. This issue is due to the fact that cascades...
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作者：Dyszewski, Piotr; Mikosch, Thomas
作者单位：University of Wroclaw; Technical University of Munich; University of Copenhagen
摘要：It is well known that the product of two independent regularly varying random variables with the same tail index is again regularly varying with this index. In this paper, we provide sharp sufficient conditions for the regular variation property of product-type functions of regularly varying random vectors, generalizing and extending the univariate theory in various directions. The main result is then applied to characterize the regular variation property of products of i.i.d. regularly varyin...
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作者：He, Yukun
作者单位：University of Zurich
摘要：We consider a class of sparse random matrices, which includes the adjacency matrix of Erdos-Renyi graphs G(N, p) for p is an element of [N epsilon-1, N-epsilon]. We identify the joint limiting distributions of the eigenvalues away from 0 and the spectral edges. Our result indicates that unlike Wigner matrices, the eigenvalues of sparse matrices satisfy central limit theorems with normalization N root p. In addition, the eigenvalues fluctuate simultaneously: the correlation of two eigenvalues o...
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作者：Landon, Benjamin; Sosoe, Philippe
作者单位：Massachusetts Institute of Technology (MIT); Cornell University
摘要：We present some applications of central limit theorems on mesoscopic scales for random matrices. When combined with the recent theory of homogenization for Dyson Brownian motion, this yields the universality of quantities which depend on the behavior of single eigenvalues of Wigner matrices and beta-ensembles. Among the results we obtain are the Gaussian fluctuations of single eigenvalues for Wigner matrices (without an assumption of 4 matching moments) and classical beta-ensembles (beta = 1, ...
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作者：Arnaudon, M.; Del Moral, P.
作者单位：Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Inria; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We propose a second order differential calculus to analyze the regularity and the stability properties of the distribution semigroup associated with McKean-Vlasov diffusions. This methodology provides second order Taylor type expansions with remainder for both the evolution semigroup as well as the stochastic flow associated with this class of nonlinear diffusions. Bismut-Elworthy-Li formulae for the gradient and the Hessian of the integro-differential operators associated with these expansion...
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作者：Lopes, Fabio; Luczak, Malwina
作者单位：Universidad Tecnologica Metropolitana; University of Melbourne
摘要：We consider a simple Markov model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in the absence of the other one is described by the stochastic SIS logistic epidemic process, and we assume that there is perfect cross-immunity between the two strains, that is, individuals infected by one are temporarily immune to re-infections and infections by the other. For the case where one strain is strictly stronger ...
