111 research outputs found

### An example of non-attainability of expected quantum information

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

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

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

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

### Plausibility functions and exact frequentist inference

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

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

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 $\rho_{\rm red}(t)$ approach the exact reduced state found via
Imamo\=glu's enlarged system method [Phys. Rev. A. 50, 3650 (1994)].Comment: 17 pages, 4 figure

- …