扩散 马尔可夫过程和鞅 第1卷

作者L.C.G.Rogers,D.Williams 著
出版社
出版时间2003-01-01

特色:

Longago(orsoitseemstoday),Chungwroteonpage196ofhisbook[1]:'Onewondersifthepresenttheoryofstochasticprocessesisnotstilltoodifficultforapplications.'Advancesinthetheorysincethattimehavebeenphenomenal,butthesehavebeenaccompaniedbyanincreaseinthetechnicaldifficultyofthesubjectsobewilderingastogiveaquaintcharmtoChung'suseoftheword'still'.Meyerwritesintheprefacetohisdefinitiveaccountofstochasticintegraltheory:'...ilfaut...uncoursdesixmoissurlesdefinitions.Quepeutonyfaire?'IhavethoughtupasintuitiveapictureofthesubjectasIcan,writtenitdownatspeed,andrefusedtobeluredbackbypiety(orevenbywit!)tocancelhalfaline.'First'intuition,whichiswhatyouneedwhenyouarelearningthesubject,israw,roughandready;and,asyouhaveguessed,Imaketheexcusethatitdemandsacompatiblestyleandlackofpolish.NotethatIwrote'firstintuition'.Consideranexample.Meyer'sconceptofarightprocessisexactlyrightforMarkovprocesstheory,buttheconceptistheresultofalongevolution.Tounderstanditproperly,youneedahighlydevelopedintuition,andthattakestimetoacquire.Thedifficultywiththebestadvancedliteratureisthatitsauthorshavetoomuchintuition;nevermakethemistakeofthinkingotherwise.

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