پديد آورنده :
پروانه ضيابري، آزاده
عنوان :
شبيه سازي توزيع هاي پايدار ملايم شده
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
آمار رياضي
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
توصيفگر ها :
تابع مشخصه , توزيع بي نهايت بار تقسيم پذير , روش نمونه گيري رد - پذيرش , توزيع پواسن مركب , فرآيند لوي
تاريخ نمايه سازي :
1394/08/06
استاد داور :
افشين پرورده، صفيه محمودي
تاريخ ورود اطلاعات :
1396/10/05
چكيده انگليسي :
On Simulation of Tempered Stable Distributions Seyedeh Azadeh Parvaneh Ziabari a parvaneh@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Ali Rejali a rejali@cc iut ac ir Advisor Dr Zahra Saberi z saberi@cc iut ac ir 2010 MSC 65C10 68U20 60E07 60B10 Keywords Stable distribution Tempered stable distribution Characteristic function In nitely divisible distribution Acceptance rejection sampling method Compound Poisson distribution L vy process Abstract In this thesis the tempered stable distributions and processes are introduced Then varioussimulation methods for tempered stable random variables with stability index greater than one andskewness parameter equals to one are investigated Special attention will be to the case of very smallscale parameters which corresponds to increments of tempered stable L vy processes with a very shortstepsize This was motivated by its application for approximating L vy driven stochastic di erentialequations such as the Euler scheme for which we have to have many small time independent incrementsof the L vy process Tempered stable random variables do not have density function in closed form Due to thisfact their simulation is a very di cult task However these variables can be simulated by usingacceptance rejection sampling method by nding some relations between their density function andother density functions which can be simulated easily According to this approach two methods whichare called exact sampling using density function and approximative sampling with stable proposaldistribution are obtained Another approach is a suitable decomposition of their L vy measures intotwo L vy measures With this decomposition a tempered stable random variable decomposes intoa constant and two random variables which are named small and large jump components There fore with simulating these two components a tempered stable random variable will be simulated
استاد داور :
افشين پرورده، صفيه محمودي
