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作者：Mania, M; Schweizer, M
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich
摘要：We study the dynamics of the exponential utility indifference value process C(B; alpha) for a contingent claim B in a semimartingale model with a general continuous filtration. We prove that C(B; alpha) is (the first component of) the unique solution of a backward stochastic differential equation with a quadratic generator and obtain BMO estimates for the components of this solution. This allows us to prove several new results about C-t (B; alpha). We obtain continuity in B and local Lipschitz...
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作者：Dupuis, P; Wang, H
作者单位：Brown University
摘要：We consider the problem of optimal stopping for a one-dimensional diffusion process. Two classes of admissible stopping times are considered. The first class consists of all nonanticipating stopping times that take values in [0, ∞], while the second class further restricts the set of allowed values to the discrete grid {nh: n = 0, 1, 2,..., ∞} for some parameter h > 0. The value functions for the two problems are denoted by V(x) and V-h(x), respectively. We identify the rate of convergence o...
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作者：Doug, R; Guillin, A; Najim, J
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Universite PSL; Universite Paris-Dauphine; Centre National de la Recherche Scientifique (CNRS); IMT - Institut Mines-Telecom; IMT Atlantique
摘要：Consider the state space model (X-t, Y-t), where (X-t) is a Markov chain, and (Y-t) are the observations. In order to solve the so-called filtering problem, one has to compute L(X-t\Y-1,..., Y-t), the law of X-t given the observations (Y-1,..., Y-t). The particle filtering method gives an approximation of the law L(X-t\Y-1,..., Y-t) by an empirical measure 1/n Sigma(1)(n)delta(xi,t). In this paper we establish the moderate deviation principle for the empirical mean 1/n Sigma(1)(n)psi(x(i,t)) (...
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作者：Fort, G; Roberts, GO
作者单位：Centre National de la Recherche Scientifique (CNRS); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Lancaster University
摘要：We derive sufficient conditions for subgeometric f-ergodicity of strongly Markovian processes. We first propose a criterion based on modulated moment of some delayed return-time to a petite set. We then formulate a criterion for polynomial f-ergodicity in terms of a drift condition on the generator. Applications to specific processes are considered, including Langevin tempered diffusions on R-n and storage models.
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作者：Bai, ZD; Hu, FF
作者单位：Northeast Normal University - China; National University of Singapore; University of Virginia
摘要：This paper studies a very general urn model stimulated by designs in clinical trials, where the number of balls of different types added to the urn at trial n depends on a random outcome directed by the composition at trials 1, 2,..., n - 1. Patient treatments are allocated according to types of balls. We establish the strong consistency and asymptotic normality for both the urn composition and the patient allocation under general assumptions on random generating matrices which determine how b...
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作者：Mora, CM
作者单位：Universidad de Concepcion
摘要：The paper deals with the numerical solution of the nonlinear lto stochastic differential equations (SDEs) appearing in the unravelling of quantum master equations. We first develop an exponential scheme of weak order I for general globally Lipschitz SDEs governed by Brownian motions. Then, we proceed to study the numerical integration of a class of locally Lipschitz SDEs. More precisely, we adapt the exponential scheme obtained in the first part of the work to the characteristics of certain fi...
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作者：Ellis, RS; Otto, PT; Touchette, H
作者单位：University of Massachusetts System; University of Massachusetts Amherst; Union College; University of London; Queen Mary University London
摘要：In this paper we give a complete analysis of the phase transitions in the mean-field Blume-Emery-Griffiths lattice-spin model with respect to the canonical ensemble, showing both a second-order, continuous phase transition and a first-order, discontinuous phase transition for appropriate values of the thermodynamic parameters that define the model. These phase transitions are analyzed both in terms of the empirical measure and the spin per site by studying bifurcation phenomena of the correspo...
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作者：Schweinsberg, J; Durrett, R
作者单位：University of California System; University of California San Diego; Cornell University
摘要：When a beneficial mutation occurs in a population, the new, favored allele may spread to the entire population. This process is known as a selective sweep. Suppose we sample n individuals at the end of a selective sweep. If we focus on a site on the chromosome that is close to the location of the beneficial mutation, then many of the lineages will likely be descended from the individual that had the beneficial mutation, while others will be descended from a different individual because of reco...
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作者：Gapeev, PV
作者单位：Russian Academy of Sciences; V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
摘要：The problem of disorder seeks to determine a stopping time which is as close as possible to the unknown time of disorder when the observed process changes its probability characteristics. We give a partial answer to this question for some special cases of Levy processes and present a complete solution of the Bayesian and variational problem for a compound Poisson process with exponential jumps. The method of proof is based on reducing the Bayesian problem to an integro-differential free-bounda...
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作者：De Donno, M; Pratelli, M
作者单位：University of Pisa
摘要：We introduce a theory of stochastic integration with respect to a family of sernimartingales depending on a continuous parameter, as a mathematical background to the theory of bond markets. We apply our results to the problem of super-replication and utility maximization from terminal wealth in a bond market. Finally, we compare our approach to those already existing in literature.
