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Nassar H.S. Haidar, Adnan M. Hamzeh, Soumaya M. Hamzeh, Edward El-Nakat

On martingales invoked by stochastic exponential and monomial densities

Keywords: Monomials, density functions; entropy, expectations, generalized moments, weak stationarity

This is an extension of a previous work of the first author [1], on monomial density functions, to study the approximation features over [a, b] of, the based on α^x exponential density functions h_α(x) when α > 0 is discrete and/or fractional. If α is discrete, a random variable of h_n(x) is proved to form a martingale over a reversed filtration and is compared with a similar situation that happens to hold with respective monomial density functions. In the case of fractional α, we advance a new stochastic operator which generates, via a nonlinear technique, unique exponential and monomial spline approximants over [a, b] to functions (x) ∈ , a certain noncommutative inner product space.

Random Operators and Stochastic Equations, Walter de Gruyter

Print ISSN: 0926-6364
Volume: 12, 12/2004
Pages: 349 - 360

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