Search results for "calculus"
showing 10 items of 617 documents
Likelihood Inference for Gibbs Processes in the Analysis of Spatial Point Patterns
2001
Plusieurs auteurs ont propose des approximations stochastiques et non-stochastiques au MLE pour les processus de Gibbs utilises pour decrire les interactions entre deux points dans une distribution spatiale de points. Cettes approximations sont necessaires a cause de la difficulte en l'evaluation de la constante qui normalise la f.d.p., Cet article present une comparaison, parmi d'un model de Strauss, des methodes qui utilisent des approximations directes aux MLE et des methodes qui utilisent techniques de Monte Carlo de chaine de Markov. Les techniques de simulation utilisees sont le Gibbs sampler et l'algorithm de Metropolis-Hastings.
A note on Malliavin smoothness on the Lévy space
2017
We consider Malliavin calculus based on the Itô chaos decomposition of square integrable random variables on the Lévy space. We show that when a random variable satisfies a certain measurability condition, its differentiability and fractional differentiability can be determined by weighted Lebesgue spaces. The measurability condition is satisfied for all random variables if the underlying Lévy process is a compound Poisson process on a finite time interval. peerReviewed
Distribucion final de referencia para el problema de Fieller-Creasy
1982
The problem of making inferences about the ratio of two normal populations is usually known as the Fieller-Creasy problem, and it gave rise to a controversy among fiducialists and confidence-intervalists. A Bayesian solution to such a problem when the two normal populations have the same unknown variance was presented by Bernardo (1977) using reference non-informative prior distributions. The solution to the case in which the variances are not assumed equal is obtained here. Some numerical results for artificial populations are given
A new stochastic representation for the decay from a metastable state
2002
Abstract We show that a stochastic process on a complex plane can simulate decay from a metastable state. The simplest application of the method to a model in which the approach to equilibrium occurs through transitions over a potential barrier is discussed. The results are compared with direct numerical simulations of the stochastic differential equations describing system's evolution. We have found that the new method is much more efficient from computational point of view than the direct simulations.
Basing the Analysis of Comparative Bioavailability Trials on an Individualized Statistical Definition of Equivalence
1993
The conventional definition of bioequivalence in terms of population means only, is criticized for lacking relevance to the individual subject. Both approaches to bioequivalence assessment proposed here for avoiding this shortcoming, focus on the probability of an event induced by the response of a randomly selected subject to two formulations of a given active agent. The first approach leads to converting the basic idea underlying the well-known 75-rule into an exact statistical procedure. The second approach is of a parametric nature. It reduces bioequivalence assessment to testing against the alternative hypothesis that the standardized expected value of a Gaussian distribution is contai…
On Limiting Fréchet ε-Subdifferentials
1998
This paper presents an e-sub differential calculus for nonconvex and nonsmooth functions. We extend the previous work by Jofre et all to the case where the functions are lower semicontinuous instead of locally Lipschitz.
Malliavin calculus of Bismut type without probability
2007
We translate in semigroup theory Bismut's way of the Malliavin calculus.
Steady-state dynamic response of various hysteretic systems endowed with fractional derivative elements
2019
In this paper, the steady-state dynamic response of hysteretic oscillators comprising fractional derivative elements and subjected to harmonic excitation is examined. Notably, this problem may arise in several circumstances, as for instance, when structures which inherently exhibit hysteretic behavior are supplemented with dampers or isolators often modeled by employing fractional terms. The amplitude of the steady-state response is determined analytically by using an equivalent linearization approach. The procedure yields an equivalent linear system with stiffness and damping coefficients which are related to the amplitude of the response, but also, to the order of the fractional derivativ…
What is Differential Stochastic Calculus?
1999
Some well known concepts of stochastic differential calculus of non linear systems corrupted by parametric normal white noise are here outlined. Ito and Stratonovich integrals concepts as well as Ito differential rule are discussed. Applications to the statistics of the response of some linear and non linear systems is also presented.
Stochastic Differential Calculus
1993
In many cases of engineering interest it has become quite common to use stochastic processes to model loadings resulting from earthquake, turbulent winds or ocean waves. In these circumstances the structural response needs to be adequately described in a probabilistic sense, by evaluating the cumulants or the moments of any order of the response (see e.g. [1, 2]). In particular, for linear systems excited by normal input, the response process is normal too and the moments or the cumulants up to the second order fully characterize the probability density function of both input and output processes. Many practical problems involve processes which are approximately normal and the effect of the…