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作者：Baudoin, F; Teichmann, J
作者单位：Technische Universitat Wien
摘要：We apply methods from Malliavin calculus to prove an infinite-dimensional version of Hormander's theorem for stochastic evolution equations in the spirit of Da Prato-Zabczyk. This result is used to show that HJM-equations from interest rate theory, which satisfy the Hormander condition, have the conceptually undesirable feature that any selection of yields admits a density as multi-dimensional random variable.
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作者：Bolthausen, E; Giacomin, G
作者单位：University of Zurich; Universite Paris Cite
摘要：We analyze a (1 + 1)-dimension directed random walk model of a polymer dipped in a medium constituted by two immiscible solvents separated by a flat interface. The polymer chain is heterogeneous in the sense that a single monomer may energetically favor one or the other solvent. We focus on the case in which the polymer types are periodically distributed along the chain or, in other words, the polymer is constituted of identical stretches of fixed length. The phenomenon that one wants to analy...
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作者：Zitkovic, G
作者单位：Carnegie Mellon University
摘要：We introduce a linear space of finitely additive measures to treat the problem of optimal expected utility from consumption under a stochastic clock and an unbounded random endowment process. In this way we establish existence and uniqueness for a large class of utility-maximization problems including the classical ones of terminal wealth or consumption, as well as the problems that depend on a random time horizon or multiple consumption instances. As an example we explicitly treat the problem...
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作者：Ata, B; Harrison, JM; Shepp, LA
作者单位：Northwestern University; Rutgers University System; Rutgers University New Brunswick; Stanford University
摘要：A system manager dynamically controls a diffusion process Z that lives in a finite interval [0, b]. Control takes the form of a negative drift rate 0 that is chosen from a fixed set A of available values. The controlled process evolves according to the differential relationship dZ = dX - theta (Z) dt + dL - dU, where X is a (0, sigma) Brownian motion, and L and U are increasing processes that enforce a lower reflecting barrier at Z = 0 and an upper reflecting barrier at Z = b, respectively. Th...
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作者：Egloff, D
摘要：We extend the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems on high-dimensional state spaces. We reformulate the optimal stopping problem for Markov processes in discrete time as a generalized statistical learning problem. Within this setup we apply deviation inequalities for suprema of empirical processes to derive consistency criteria, and to estimate the convergence rate and sample complexity. Our results strengthen and extend earlier results obtained by C...
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作者：Lambert, A
作者单位：Universite PSL; Ecole Normale Superieure (ENS); Sorbonne Universite; Sorbonne Universite
摘要：In order to model random density-dependence in population dynamics, we construct the random analogue of the well-known logistic process in the branching process' framework. This density-dependence corresponds to intraspecific competition pressure, which is ubiquitous in ecology, and translates mathematically into a quadratic death rate. The logistic branching process, or LB-process, can thus be seen as (the mass of) a fragmentation process (corresponding to the branching mechanism) combined wi...
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作者：Arora, S; Kannan, R
作者单位：Princeton University; Yale University
摘要：Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a local-search heuristic from Dempster, Laird and Rubin [J. Roy. Statist. Soc. Ser B 39 (1977) 1-38]. These do not provably run in polynomial time. We present the first algorithm that provably learns the component Gaussians in time that is polynomial in the dimension. ...
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作者：Baxendale, PH
作者单位：University of Southern California
摘要：We give computable bounds on the rate of convergence of the transition probabilities to the stationary distribution for a certain class of geometrically ergodic Markov chains. Our results are different from earlier estimates of Meyn and Tweedie, and from estimates using coupling, although we start from essentially the same assumptions of a drift condition toward a small set. The estimates show a noticeable improvement on existing results if the Markov chain is reversible with respect to its st...
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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...
