discrete time first order difference equations

《discrete time first order difference equations》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、ChapterDiscreteTime:First-OrderDifferenceEquationsInthecontinuous-timecontext,thepatternofchangeof'avariableyisembodiedinthederivathcsrl(l),y"(t}.etc.Thetimechangeim'olvedintheseisoccurringcontinuously.Whentimeis,instead,takentobeadiscretevariable,sothatthevariablef

2、ISallowedtotukl.::integervaluesonly,theconceptoflhederivativeobviouslywillnolongerbeappropriate.Then,asweshallsec,thepatternof.:hangellfthevariableymustbedescribedby50-culleddIfferences,ratherthanbyderivativesordifferentials,ofy(f).Accordingly,thetcclmiquesofdiffere

3、ntialequationswillgivewaytothoseofdi[k:!'enceequations.WhenweafCdealingwithdiscretetime,lhevalueofvariableywillchangeonlywhenthevarinbletCh'lllgl'~fromnDl'integervaluetothene>.t.suchasfwmI=Itotc::.2.Meanwhile,nothingissupp{)~cdtohappentoy.Inthislight,itbecomesmorecn

4、mcnienttointerpretthevaluc~oftasrcferringtoperiods-ratherthanpoints-oftime,witht=1denotingperiod1andt=2denolingperiod2.andsofonh.Thenwelllaysimplyregardyashavingoneuniquevalueincachtimeperiod.Inviewofthisinterpretation,thediscrete•timeversionofeconomicdynamicsisotte

5、nreferredtoasperiodanalysi,'.Itshouldbeemph'1.sized,however,that"pcriod"isbeingusedherenotinthecalendarsenscbutintheanalyticalsense.lIenee,aperiodmayinvolveoneextentofcalendartimeinaparticulareconomicmodel,butanaltogetherdifferentoneinanother.Eveninthesamemodel,more

6、~over,euchsuccessiveperiodshmlldnotnecessarilybeconstrueda~meaningequalcalellwdartime.Intheanalyticalsense,aperiNiismerelyalengthoftimethatelapse~beforethevariable}'undergoesachange.17.1DiscreteTime,Differences,andDifferenceEguati0tlsmThechangefromcomiulLoUStimetodi

7、scretetimeproducesnoeffectonthefundamentalnatureofdynamicanalysis,althoughtheformulationoftheprobh::mmustbcaltered.Basi•cally.ourdynamicproblemisstilltofindatimepathfromS()ll1Cgivenpatternofchangeof(tvariableyovertime,Butthepattern{Ifchange~h(luldl1{lVberepresented

8、bythediffer•encequotientD..y/!::r.t,whichisthediscrete-timecountcrpartofthederivativedy/dt,RecalLhowever.thattcannowtukeonlyintegcrvalues;