Stokhasticheskie Differentsial'Nye Uravneniya S Semimartingalami

Algebra obobshchennykh sluchaynykh protsessov pozvolyaet izuchat' razlichnye tipy stokhasticheskikh differentsial'nykh uravneniy s edinykh pozitsiy. Odnako vazhno znat', pri kakikh usloviyakh element algebry obobshchennykh sluchaynykh protsessov assotsiiruet obychnyy sluchaynyy protsess. Takie usloviya pozvolyayut perekhodit' ot edinoy teorii k chastnym sluchayam, predlagaya bolee detal'noe opisanie dinamiki modeliruemoy sistemy. Dannaya kniga posvyashchena postroeniyu assotsiirovannykh resheniy stokhasticheskikh differentsial'nykh uravneniy s semimartingalami. Pervaya glava soderzhit opisanie ispol'zuemykh ponyatiy i konstruktsiy. Vo vtoroy glave provoditsya postroenie sluchaynykh protsessov, assotsiirovannykh obobshchennymi stokhasticheskimi integralami po protsessu ogranichennoy variatsii, nepreryvnomu martingalu, semimartingalu. V tret'ey glave dana polnaya klassifikatsiya assotsiirovannykh resheniy neavtonomnykh uravneniy v differentsialakh, soderzhashchikh obobshchennyy sluchaynyy protsess ogranichennoy variatsii.