The Marginal Density of a TMA(1) Process

2020 ◽  
Vol 41 (3) ◽  
pp. 476-484
Author(s):  
Dong Li ◽  
Jiaming Qiu
Keyword(s):  
Marginal Density

scholarly journals Quantifying the closeness to a set of random curves via the mean marginal likelihood

2020 ◽  
Author(s):  
Cédric Rommel ◽  
Joseph Frédéric Bonnans ◽  
Baptiste Gregorutti ◽  
Pierre Martinon
Keyword(s):  
Marginal Likelihood ◽  
Marginal Density ◽  
Random Curves ◽  
Practical Applications ◽  
Random Functions ◽  
Practical Usefulness ◽  
Class Of Estimators ◽  
The Mean ◽  
Multivariate Density ◽  
Aircraft Trajectories

In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.

Marginal Density Expansions for Diffusions and Stochastic Volatility II: Applications

2013 ◽  
Vol 67 (2) ◽  
pp. 321-350 ◽  
Author(s):  
J. D. Deuschel ◽  
P. K. Friz ◽  
A. Jacquier ◽  
S. Violante
Keyword(s):  
Stochastic Volatility ◽  
Marginal Density ◽  
Density Expansions

On Marginal Density Functions of Continuous Densities II

1977 ◽  
Vol 84 (5) ◽  
pp. 364-365
Author(s):  
M. J. Pelling ◽  
Albert Verbeek
Keyword(s):  
Density Functions ◽  
Marginal Density

scholarly journals OVERRIDING THE EXPERTS: A FUSION METHOD FOR COMBINING MARGINAL CLASSIFIERS

2001 ◽  
Vol 10 (01n02) ◽  
pp. 157-179
Author(s):  
MARK D. HAPPEL ◽  
PETER BOCK
Keyword(s):  
Joint Probability ◽  
Probability Density Functions ◽  
Density Functions ◽  
Marginal Density ◽  
Multiple Features ◽  
Probability Of Error ◽  
Voting Methods ◽  
Asymptotic Probability ◽  
Joint Probability Density ◽  
Optimal Bayesian Classifier

The design of an optimal Bayesian classifier for multiple features is dependent on the estimation of multidimensional joint probability density functions and therefore requires a design sample size that increases exponentially with the number of dimensions. A method was developed that combines classification decisions from marginal density functions using an additional classifier. Unlike voting methods, this method can select a more appropriate class than the ones selected by the marginal classifiers, thus "overriding" their decisions. It is shown that this method always exhibits an asymptotic probability of error no worse than the probability of error of the best marginal classifier.

scholarly journals Joint distribution of a Lévy process and its running supremum

2018 ◽  
Vol 55 (2) ◽  
pp. 488-512 ◽  
Author(s):  
Laure Coutin ◽  
Monique Pontier ◽  
Waly Ngom
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Weak Solution ◽  
Diffusion Process ◽  
Lebesgue Measure ◽  
Joint Distribution ◽  
Random Variable ◽  
Jump Diffusion ◽  
Marginal Density ◽  
The Law

Abstract Let X be a jump-diffusion process and X* its running supremum. In this paper we first show that for any t > 0, the law of the pair (X*t, Xt) has a density with respect to the Lebesgue measure. This allows us to show that for any t > 0, the law of the pair formed by the random variable Xt and the running supremum X*t of X at time t can be characterized as a weak solution of a partial differential equation concerning the distribution of the pair (X*t, Xt). Then we obtain an expression of the marginal density of X*t for all t > 0.

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