
doob-mayer vighadana sidhaantham

oru martingalinte thukayum vardhichuvarunna pravachanatheethamaaya prakriya aayi oru submartingaline savisheshamaaya reethiyil vighadippikkaavunna avasthakal prasthaavikkunna stokkaastik calculusile oru sidhaanthamaanu doob-mayer decomposition sidhaantham. joseph ell. yude perilaanu ithu ariyappedunnathu. doob, pooll-andrey mayer.
charithram.
1953ll doob decomposition sidhaantham prasidheekarichu, ithu chila vyathirikthamaya samaya martingalukalkku savisheshamaaya vighadanam nalkunnu. addeham sidhaanthathinte oru thudarchayaaya samaya pathipp oohikkukayum 1962lum 1963lum pooll-andrey mayer prasidheekaricha rund prasidheekaranangalil atharamoru sidhaantham theliyikkukayum athu doob-mayer vighadanam ennariyappedukayum cheythu. doobinte bahumaanaartham, mayer thante athulyamaaya vighadana sidhaantham prayogicha supermartingelukalu classine soochippikkaan "klaas dii" enna padam upayogichu.
klaas dii supermartingles.
formula 2 umm shekharavum aanenkil oru cadlag supermartingal formula _ 1 klaas dii aanu
ithu orepole samyojippikkaavunnathaan.
sidhaantham.
formula _ 4 klaas dii yude cadlag supermartingal ayirikkatte. appol formula 6 ulla savisheshavum vardhikkunnathum pravachikkavunnathumaaya oru prakriya formula undu, athaayath formula 7 oru ekeekritha martingal aanu.

