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Chein-Steinova metoda : magistrsko delo
Raič, Martin
Delo obravanava Chen-Steinovo metodo, ki pomeni preokret pri aproksimaciji porazdelitev vsot slučajnih spremenljivk s Poissonovo, normalno ali tudi kako drugo "limitno" porazdelitvijo. Glavni ...prednosti te metode sta, da dá eksplicitno oceno napake in da ne deluje le za vsote neodvisnih, temveč tudi rahlo odvisnih slučajnih spremenljivk. Ko porazdelitev dane slučajne spremenljivke ▫$X$▫ aproksimiramo z bolj znano porazdelitvijo ▫$\mu$▫, napako ocenjujemo z izrazi ▫$|E(f(X)) - \int f\;d\mu|$▫ za primeren razred testnih funkcij ▫$f$▫. Osnovna ideja Chen-Steinove metode je, da poiščemo markovski (Feller-Dynkiov) proces, ki ima porazdelitev ▫$\mu$▫ za ravnovesno, in rešimo Steinovo enačbo ▫$Gg=f-\int f\; d\mu$▫, kjer je ▫$G$▫ generator operatorske polgrupe, ki pripada našemu markovskemu procesu. Tedaj velja ▫$E(f(X))-\int f \; d\mu = E(Gg)(X)$▫, torej je dovolj oceniti slednji izraz. Izkaže se, da je to bistveno lažje od ocene prvotnega izraza. Delo predstavi aproksimacijo s Poissonovo in normalno porazdelitvijo, čeprav Chen-Steinova metoda nikakor ni omejena le na aproksimacijo s tema dvema porazdelitvama. Pri Poissonovi aproksimaciji navede tudi dva zgleda z odvisnimi slučajnimi porazdelitvami. Predstavi pa tudi markovske procese, ki tičijo v ozadju Chen-Steinove metode.
Type of material - master's thesis
Publication and manufacture - Ljubljana : [M. Raič], 1998
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