caa a22 4500 378920774 CHVBK 20180305123604.0 cr unu---uuuuu 161128e20041201xx s 000 0 eng 10.1515/1569397042722382 doi (NATIONALLICENCE)gruyter-10.1515/1569397042722382 On martingales invoked by stochastic exponential and monomial densities [Elektronische Daten] [Nassar H.S. Haidar, Adnan M. Hamzeh, Soumaya M. Hamzeh, Edward El-Nakat] 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 αx exponential density functions hα (x) when α > 0 is discrete and/or fractional. If α is discrete, a random variable of hn (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. Copyright 2003, Walter de Gruyter Monomials nationallicence density functions nationallicence entropy nationallicence expectations nationallicence generalized moments nationallicence weak stationarity nationallicence Haidar Nassar H.S. Center for Research in Applied Mathematics and Statistics (CRAMS), Department of Basic Sciences, Business and Computer University College (BCU), Beirut, Lebanon aut Hamzeh Adnan M. Center for Research in Applied Mathematics and Statistics (CRAMS), Department of Basic Sciences, Business and Computer University College (BCU), Beirut, Lebanon aut Hamzeh Soumaya M. Center for Research in Applied Mathematics and Statistics (CRAMS), Department of Basic Sciences, Business and Computer University College (BCU), Beirut, Lebanon aut El-Nakat Edward Center for Research in Applied Mathematics and Statistics (CRAMS), Department of Basic Sciences, Business and Computer University College (BCU), Beirut, Lebanon aut Random Operators and Stochastic Equations Walter de Gruyter 12/4(2004-12-01), 349-360 0926-6364 12:4<349 2004 12 rose https://doi.org/10.1515/1569397042722382 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/1569397042722382 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Haidar Nassar H.S. Center for Research in Applied Mathematics and Statistics (CRAMS), Department of Basic Sciences, Business and Computer University College (BCU), Beirut, Lebanon aut NATIONALLICENCE 700 1- Hamzeh Adnan M. Center for Research in Applied Mathematics and Statistics (CRAMS), Department of Basic Sciences, Business and Computer University College (BCU), Beirut, Lebanon aut NATIONALLICENCE 700 1- Hamzeh Soumaya M. Center for Research in Applied Mathematics and Statistics (CRAMS), Department of Basic Sciences, Business and Computer University College (BCU), Beirut, Lebanon aut NATIONALLICENCE 700 1- El-Nakat Edward Center for Research in Applied Mathematics and Statistics (CRAMS), Department of Basic Sciences, Business and Computer University College (BCU), Beirut, Lebanon aut NATIONALLICENCE 773 0- Random Operators and Stochastic Equations Walter de Gruyter 12/4(2004-12-01), 349-360 0926-6364 12:4<349 2004 12 rose CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter