111 research outputs found

    An example of non-attainability of expected quantum information

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    Introduction Braunstein and Caves [1] have clarified the relation between classical expected information i(`), in the sense of Fisher, and the analogous concept of expected quantum information I(`), by showing that I(`) is an upper bound of i(`; M) with respect to all (dominated) generalized measurements M of the state ae = ae(`) where ` is an unknown parameter and i(`; M) is the Fisher expected information for ` in the distribution of the outcome of the measurement of M . They indicate moreover that a measurement exists achieving the bound. In the present paper we show by an example, for an elementary spin- 1 2 situation, that in general there does not exist

    Bridge homogeneous volatility estimators

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    We present a theory of bridge homogeneous volatility estimators for log-price stochastic processes. Starting with the standard definition of a Brownian bridge as the conditional Wiener process with two endpoints fixed, we introduce the concept of an incomplete bridge by breaking the symmetry between the two endpoints. For any given time interval, this allows us to encode the information contained in the open, high, low and close prices into an incomplete bridge. The efficiency of the new proposed estimators is favourably compared with that of the classical Garman–Klass and Parkinson estimators

    Importance Sampling for multi-constraints rare event probability

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    Improving Importance Sampling estimators for rare event probabilities requires sharp approx- imations of the optimal density leading to a nearly zero-variance estimator. This paper presents a new way to handle the estimation of the probability of a rare event defined as a finite intersection of subset. We provide a sharp approximation of the density of long runs of a random walk condi- tioned by multiples constraints, each of them defined by an average of a function of its summands as their number tends to infinity.Comment: Conference pape

    Meixner class of non-commutative generalized stochastic processes with freely independent values I. A characterization

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    Let TT be an underlying space with a non-atomic measure σ\sigma on it (e.g. T=RdT=\mathbb R^d and σ\sigma is the Lebesgue measure). We introduce and study a class of non-commutative generalized stochastic processes, indexed by points of TT, with freely independent values. Such a process (field), ω=ω(t)\omega=\omega(t), tTt\in T, is given a rigorous meaning through smearing out with test functions on TT, with Tσ(dt)f(t)ω(t)\int_T \sigma(dt)f(t)\omega(t) being a (bounded) linear operator in a full Fock space. We define a set CP\mathbf{CP} of all continuous polynomials of ω\omega, and then define a con-commutative L2L^2-space L2(τ)L^2(\tau) by taking the closure of CP\mathbf{CP} in the norm PL2(τ):=PΩ\|P\|_{L^2(\tau)}:=\|P\Omega\|, where Ω\Omega is the vacuum in the Fock space. Through procedure of orthogonalization of polynomials, we construct a unitary isomorphism between L2(τ)L^2(\tau) and a (Fock-space-type) Hilbert space F=Rn=1L2(Tn,γn)\mathbb F=\mathbb R\oplus\bigoplus_{n=1}^\infty L^2(T^n,\gamma_n), with explicitly given measures γn\gamma_n. We identify the Meixner class as those processes for which the procedure of orthogonalization leaves the set CP\mathbf {CP} invariant. (Note that, in the general case, the projection of a continuous monomial of oder nn onto the nn-th chaos need not remain a continuous polynomial.) Each element of the Meixner class is characterized by two continuous functions λ\lambda and η0\eta\ge0 on TT, such that, in the F\mathbb F space, ω\omega has representation \omega(t)=\di_t^\dag+\lambda(t)\di_t^\dag\di_t+\di_t+\eta(t)\di_t^\dag\di^2_t, where \di_t^\dag and \di_t are the usual creation and annihilation operators at point tt

    Plausibility functions and exact frequentist inference

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    In the frequentist program, inferential methods with exact control on error rates are a primary focus. The standard approach, however, is to rely on asymptotic approximations, which may not be suitable. This paper presents a general framework for the construction of exact frequentist procedures based on plausibility functions. It is shown that the plausibility function-based tests and confidence regions have the desired frequentist properties in finite samples---no large-sample justification needed. An extension of the proposed method is also given for problems involving nuisance parameters. Examples demonstrate that the plausibility function-based method is both exact and efficient in a wide variety of problems.Comment: 21 pages, 5 figures, 3 table

    Stochastic particle packing with specified granulometry and porosity

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    This work presents a technique for particle size generation and placement in arbitrary closed domains. Its main application is the simulation of granular media described by disks. Particle size generation is based on the statistical analysis of granulometric curves which are used as empirical cumulative distribution functions to sample from mixtures of uniform distributions. The desired porosity is attained by selecting a certain number of particles, and their placement is performed by a stochastic point process. We present an application analyzing different types of sand and clay, where we model the grain size with the gamma, lognormal, Weibull and hyperbolic distributions. The parameters from the resulting best fit are used to generate samples from the theoretical distribution, which are used for filling a finite-size area with non-overlapping disks deployed by a Simple Sequential Inhibition stochastic point process. Such filled areas are relevant as plausible inputs for assessing Discrete Element Method and similar techniques

    A perturbative approach to non-Markovian stochastic Schr\"odinger equations

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    In this paper we present a perturbative procedure that allows one to numerically solve diffusive non-Markovian Stochastic Schr\"odinger equations, for a wide range of memory functions. To illustrate this procedure numerical results are presented for a classically driven two level atom immersed in a environment with a simple memory function. It is observed that as the order of the perturbation is increased the numerical results for the ensembled average state ρred(t)\rho_{\rm red}(t) approach the exact reduced state found via Imamo\=glu's enlarged system method [Phys. Rev. A. 50, 3650 (1994)].Comment: 17 pages, 4 figure
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