The indeterminate Hamburger moment problem is considered, jointly with all its real axis supported probability density functions. As a consequence of entropy functional concavity, out of such densities there is one which has largest entropy and that plays a fundamental role: we call it 𝑓h𝑚𝑎𝑥. It is proved that the approximate Maximum Entropy (MaxEnt) densities constrained by an increasing number of moments converge in entropy to 𝑓h𝑚𝑎𝑥 where the value of its entropy can be finite or −∞.
Indeterminate Hamburger moment problem: Entropy convergence / Novi Inverardi, P. L.; Tagliani, A.; Milev, M.. - In: STATISTICS & PROBABILITY LETTERS. - ISSN 0167-7152. - STAMPA. - 212:(2024), pp. 1-6. [10.1016/j.spl.2024.110155]
Indeterminate Hamburger moment problem: Entropy convergence
Novi Inverardi P. L.
Primo
;Tagliani A.Secondo
;Milev M.Ultimo
2024-01-01
Abstract
The indeterminate Hamburger moment problem is considered, jointly with all its real axis supported probability density functions. As a consequence of entropy functional concavity, out of such densities there is one which has largest entropy and that plays a fundamental role: we call it 𝑓h𝑚𝑎𝑥. It is proved that the approximate Maximum Entropy (MaxEnt) densities constrained by an increasing number of moments converge in entropy to 𝑓h𝑚𝑎𝑥 where the value of its entropy can be finite or −∞.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
