aches ▁to ▁path ▁integr als ▁ ▁Function al ▁integr als ▁where ▁the ▁space ▁of ▁integration ▁consists ▁of ▁paths ▁( ν ▁= ▁ 1 ) ▁can ▁be ▁defined ▁in ▁many ▁different ▁ways . ▁ ▁The ▁definitions ▁fall ▁in ▁two ▁different ▁classes : ▁the ▁constru ctions ▁derived ▁from ▁Wiener ' s ▁theory ▁yield ▁an ▁integral ▁based ▁on ▁a ▁measure , ▁whereas ▁the ▁constru ctions ▁following ▁Fe yn man ' s ▁path ▁integral ▁do ▁not . ▁ ▁Even ▁within ▁these ▁two ▁broad ▁divisions , ▁the ▁integr als ▁are ▁not ▁identical , ▁that ▁is , ▁they ▁are ▁defined ▁differently ▁for ▁different ▁classes ▁of ▁functions . ▁ ▁The ▁Wiener ▁integral ▁ ▁In ▁the ▁Wiener ▁integral , ▁a ▁probability ▁is ▁assigned ▁to ▁a ▁class ▁of ▁Brown ian ▁motion ▁paths . ▁ ▁The ▁class ▁consists ▁of ▁the ▁paths ▁w ▁that ▁are ▁known ▁to ▁go ▁through ▁a ▁small ▁region ▁of ▁space ▁at ▁a ▁given ▁time . ▁ ▁The ▁passage ▁through ▁different ▁regions ▁of ▁space ▁is ▁assumed ▁independent ▁of ▁each ▁other , ▁and ▁the ▁distance ▁between ▁any ▁two ▁points ▁of ▁the ▁Brown ian ▁path ▁is ▁assumed ▁to ▁be ▁Gaussian - dist ributed ▁with ▁a ▁variance ▁that ▁depends ▁on ▁the ▁time ▁t ▁and ▁on ▁a ▁diffusion ▁constant ▁D : ▁ ▁The ▁probability ▁for ▁the ▁class ▁of ▁paths ▁can ▁be ▁found ▁by ▁multip lying ▁the ▁prob abilities ▁of ▁starting ▁in ▁one ▁region ▁and ▁then ▁being ▁at ▁the ▁next . ▁ ▁The ▁Wiener ▁measure ▁can ▁be ▁developed ▁by ▁considering ▁the ▁limit ▁of ▁many ▁small ▁regions . ▁▁ ▁It ō ▁and ▁Str aton ov ich ▁calculus