10093

9323

كارشناسي ارشد

آمار

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1393

ده، 84ص.: مصور، جدول، نمودار

ص.ع. به فارسي و انگليسي

صفيه محمودي

علي رجالي

30/2/94

افشين پرورده، زهرا صابري

1396/09/27

كتابنامه

علوم رياضي

رياضي

ID9323

Large Deviations Technique in Stochastic Processes Particularly Poisson Cluster Processes Hossein Mohammadi hossein mohammadi1@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Sa eh Mahmoodi mahmoodi@cc iut ac ir Advisor Dr Ali Rejali a rejali@cc iut ac ir 2010 MSC 60F10 60G55 Keywords Large deviations Poisson cluster processes Hawkes processes Abstract Imagine that an insurance company collects premiums at a steady rate of a per month Let Xkbe the random amount that the insurance company has to pay out in month k to cover customerclaims Let Sn X1 Xn be the total pay out in n months Naturally the premiums must coverthe average outlays so a E Xk The company stays solvent as long as Sn na Quantifying thechances of the rare event Sn na are then of obvious interest The theory of large deviations deals with the probabilities of rare events or uctuations that areexponentially small as a function of some parameter for example the event Sn na is the above Wealso for example when we are concern on the number of random components of a system the timeover which a stochastic system is observed or the temperature of a chemical reaction The theoryhas applications in many di erent scienti c elds ranging from queuing theory to statistics and from nance to engineering Poisson cluster processes are one of the most important classes of point process models see Daley andVere Jones 2003 and Mller Waagepetersen 2004 They are natural models for the location of objectsin the space and are widely used in point process studies whether theoretical or applied Very popularand versatile Poisson cluster processes are the so called self exciting or Hawkes processes From atheoretical point of view Hawkes processes combine both a Poisson cluster process representation and

صفيه محمودي

علي رجالي

افشين پرورده، زهرا صابري