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Unformatted text preview: SlidesforMAD5932-01, SCS-MATHFSUTallahassee ∗ Prof.R.Tempone Version:ThursdayAugust31,2006 ∗ Basedonthelecturenotes StochasticandPartial DifferentialEquationswithAdaptedNumerics, byJ. Goodman,K.-S.Moon,A.Szepessy,R.Tempone, G.Zouraris. Aug29,2006-Classcontents: 1.CourseIntroduction,Admindetails 2.Motivatingexamples(Chapter1) 3.BriefProbabilityreview 1 Admindetails-syllabus-classlocation-studentgroups,emaillist,orderofgroups forassignments-HMW presentationsbygroupsonThurs- days./HandindaysareTuesdaysforthe groupthatmakesthepresentation/ 2-Matlabaccess,SCScomputerfacilities,per- sonalaccounts.-coursewebpage Coursegoal:tounderstandnumericalmeth- odsforproblemsformulatedbystochastic orpartialdifferentialequationsmodelsinsci- ence,engineeringandmathematicalfinance. 3 Motivatingexamples(Chapter1) 4 Example1(NoisyEvolutionofStockValues) Denotestockvalueby S ( t ) . Assumethat S ( t ) satisfiesthedifferentialequation dS dt = a ( t ) S ( t ) , whichhasthesolution S ( t )= e R t a ( u ) du S (0) . Sincewedonotknowpreciselyhow S ( t ) evolveswewouldliketogeneralizethemodel toastochasticsetting a ( t )= r ( t )+” noise ” . 5 Forinstance,wewillconsider dS ( t )= r ( t ) S ( t ) dt + σS (...
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