Measurements Of Relative Probabilities Research Articles

Observers and relative entropy of G-sets

In the current study, a new type of relative entropy is presented through observable objects in quantum mechanics as the probability measures. The relative probability measures as an extension of probability measures are considered via one-dimensional observers. The notion of relative entropy of the semigroup on a relative measure space is introduced using the mathematical modeling of an observable object. Moreover, it is proved that this nonnegative quantity is invariant under $$(\Theta _1 ,\Theta _2 )$$-isomorphism. Finally, we applied this concept to specific semigroups to extract Kolmogorov entropy of a dynamical system as a special case.

Invariant relative probability measures for discrete dynamical systems created by maps

In this paper we consider the maps which preserve a relative probability measure on a set M. We prove that a mapping g : M → M preserves a relative probability measure if and only if , for each simple function . We also prove that g preserves for each observer , if and only if g has a fixed point. We show that if there is x in M such thatfor each , then there is a mapping f : M → M such that g preserves .

Observable objects, observers and the integral created by them

This paper begins with the consideration of observable objects in quantum mechanics as the probability measures. Via multi-dimensional observers, relative probability measures as an extension of probability measures are considered. Order creators are introduced and by using them a new kind of integral is introduced and its essential properties are proved.

Ross recovery with recurrent and transient processes

Quantitative finance theory involves two related probability measures: a risk-neutral measure and an objective measure. The risk-neutral measure determines the prices of assets and options in a fin...

Sequential Monte Carlo Methods for Option Pricing

In this article, we provide a review and development of sequential Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte Carlo-based algorithms, that are designed to approximate expectations w.r.t a sequence of related probability measures. These approaches have been used successfully for a wide class of applications in engineering, statistics, physics, and operations research. SMC methods are highly suited to many option pricing problems and sensitivity/Greek calculations due to the nature of the sequential simulation. However, it is seldom the case that such ideas are explicitly used in the option pricing literature. This article provides an up-to-date review of SMC methods, which are appropriate for option pricing. In addition, it is illustrated how a number of existing approaches for option pricing can be enhanced via SMC. Specifically, when pricing the arithmetic Asian option w.r.t a complex stochastic volatility model, it is shown that SMC methods provide additional strategies to improve estimation.

Experimental studies of inelastic X-ray and γ-ray scattering

Studies of inelastic scattering of X-rays and γ-rays of energies higher than 30 keV performed with the help of NaI(Tl) and semi-conductor detectors of moderate and good resolution, respectively, are considered in the first part of this review. Theoretical treatments based on the non-relativistic ( e 2/2 mc 2) A 2 interaction term, the impulse approximation, the incoherent scattering function approximation, the (− e/ mc) P·A interaction term, and the relativistic second order S matrix approach have been used to understand a few representative experimental results concerning Compton scattering from K- and L-shells, and from whole atoms for values of the momentum transfer parameter x larger than about 2 Å −1, where x = sin( θ/2)/ λ, θ is the scattering angle and λ is the wavelength of the incident radiation. Techniques of detection of recoil ions have been described in the context of recent measurements of relative probabilities for double and single ionization in Compton scattering from helium. The second part of this review deals with high resolution measurements concerning inelastic scattering of X-rays of energies lower than about 20 keV. A recently demonstrated dependence of K and L X-ray fluorescence spectra on incident photon energy near respective thresholds is highlighted along with its explanation based on crystal momenta and a single step resonant inelastic scattering treatment. Non-resonant inelastic scattering studies involving the excitation of plasmons and phonons in condensed matter are also discussed. Nonlinear photon-density dependent effects interpreted as Compton scattering, and final remarks are then presented.

Key-peck probability and topography in a concurrent variable-interval variable-interval schedule with food and water reinforcers.

The relation between variables that modulate the probability and the topography of key pecks was examined using a concurrent variable-interval variable-interval schedule with food and water reinforcers. Measures of response probability (response rates, time allocation) and topography (peck duration, gape amplitude) were obtained in 5 water- and food-deprived pigeons. Key color signaled reinforcer type. During baseline, response rates and time allocations were greater to the food key than to the water key, and food-key pecks had larger gapes and shorter durations. Relative probability measures (for the food key) were increased by prewatering and decreased by prefeeding. Deprivation effects upon topography measures were apparent only when food- and water-key pecks were analyzed separately. Food-key gape amplitudes increased with prewatering and decreased with prefeeding. The clearest effect occurred with prewatering. There were no consistent effects upon water-key gapes. The key color-reinforcer relation was reversed for 3 pigeons to determine how response topography was modulated during the transition from food- to water-key pecks. Reacquisition was faster for the probability than for the topography measures. Analysis of gape-amplitude distributions during reversal indicated that response-form modulation proceeded through the generation of intermediate gape sizes.

Asymptotic analysis of Gaussian integrals. I. Isolated minimum points

This paper derives the asymptotic expansions of a wide class of Gaussian function space integrals under the assumption that the minimum points of the action are isolated. Degenerate as well as nondegenerate minimum points are allowed. This paper also derives limit theorems for related probability measures which correspond roughly to the law of large numbers and the central limit theorem. In the degenerate case, the limits are non-Gaussian.

Asymptotic analysis of Gaussian integrals, II: Manifold of minimum points

This paper derives the asymptotic expansions of a wide class of Gaussian function space integrals under the assumption that the minimum points of the action form a nondegenerate manifold. Such integrals play an important role in recent physics. This paper also proves limit theorems for related probability measures, analogous to the classical law of large numbers and central limit theorem.

A Measurement of the Absolute Probability ofK-Electron Ionization of Silver by Cathode Rays

The method of Ross's balanced foils was used to separate the $K\ensuremath{\alpha}$ quanta from the thin silver foil target radiation. The x-ray energy was absorbed in C${\mathrm{H}}_{3}$Br and S${\mathrm{O}}_{2}$ in a standard ionization chamber and the ionization currents measured by means of a Compton electrometer and calibrated ionization system. Stockmeyer's value for the energy per ion pair for these gases was used to compute the number of quanta absorbed in the chamber. The number of Ag $K$ ionizations per bombarding electron was then calculated, after the necessary target and absorption corrections. Measurements were made on 10 thin targets of average thickness 0.17 micron, and the $K$-electron ionization cross section for silver for 70.0 kv electrons was determined to be $\ensuremath{\Phi}(U)=(4.80\ifmmode\pm\else\textpm\fi{}0.43)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}$ ${\mathrm{cm}}^{2}$. The measurements of relative probabilities of $K$ electron ionization for silver by Webster, Hansen and Duveneck are normalized at 70.0 kv, ($U=2.75$) by the above value of $\ensuremath{\Phi}(U)$, and these experimental data compared with classical quantum theory and the wave mechanics theories of Massey, Mohr and Burhop, Soden and Wetzel. The theories of Soden and Wetzel compare more favorably with the experimental data than those of Massey, Mohr and Burhop, or indeed with the classical theory.