隨機互惠系統(tǒng)持久性及其參數(shù)的極大似然估計.pdf

1、學(xué)校代碼：一10200分類號：業(yè)研究生學(xué)號：密級⑨200521036無東牡埽蘊太芬碩士學(xué)位論文隨機互惠系統(tǒng)持久性及其參數(shù)的極大似然估計PersistenceofStochasticMutualismSystemandMLEofItsParameters作者：李海紅指導(dǎo)教師學(xué)科專業(yè)研究力向?qū)W位類型蔣達(dá)清教授應(yīng)用數(shù)學(xué)常微分方程學(xué)歷碩士東北師范大學(xué)學(xué)位評定委員會2007年4月AbstractThestudyaboutmathematicalb

2、iologybecomemoreandmoreimportantinthe21thcenturyTheintersectantdomainwillberesearchedmainlybetweenmathematicalbiologyandothersubjectsComparedwiththedeterminatemathematicalbiologymodel，speciesecologysystemsareoftensubject

3、toenvironmentalnoise，itisimportanttodiscoverwhetherthepresenceofasuchnoiseaffectstheseresultsthatwehaveobtainedMoreovertheestimatingoftheparametersbyapplyingstatisticalmethodswillbecomeanimportantdisscussionwithapplyings

4、tochasticdifferentialequationextensivelyinthemathematicalbiologyThispaperdiscussesarandomized2speciesLotkaVolterramutualismsystemfdzl(t)=。lO)【pl～alibi(t)a12x2(t))dt—alxl(t)dBl(t)】【dx2(t)=石2(t)【(r2a2lXl(t)一a2222(t))dt—a2x

5、2(t)dB2(t)】whereri，aij，吼0(i，J=1，2)，andBi(t)areindependentstandardBrownianmotions，i=12WeshowthatthepositivesolutionoftheassociatedstochasticdifferentialequationdoesnotexplodetoinfinityinafinitetimeInaddition，theexistence，

6、uniqueness，persistenceofthepositivesolutionsofthesystemarestudiedIngeneral，thegrowthrate，deathrateandthestrengthofwhitenoiseinthesystemareunknownMakinguseofstatisticsmethodtoestimatetheparametersinBiologyicalmodelshasbec

7、omeanewresearchtopic，howevertheproblemestimatingparametersinBiologyicalmodelistotallydifferentfromtheprobleminfinance，InthelastsectionwegivetheMLEoftheparametersinsystemThispaperiscomposedoftwopartsInthefirstchapter，wein

8、troducethehistoricalbackgroundoftheproblemswhichwillbeinvestigatedandthemainresultsofthispaperInthesecondchapter，insection21，theexistenceandtheuniquenessofpositivesolutionstoequation(12)arestudiedwhichisfundamentalforthe

9、subsequentdevelopmentsInsection22westudythepersistenceofthesolutionbyusinginequalityofChebandtheboundednessofP—thmomentsof甄and1／xiAtlast，sincetheparametersareusuallyunknown，SOwegivetheMLEsofparametersSimulationresultssho