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Lévy processes
Honzl, Ondřej ; Prokešová, Michaela (referee) ; Beneš, Viktor (advisor)
In the present thesis a short introduction into the theory of L'evy processes and subordinators is mentioned. It contains also basic results from the theory of point processes, especially of the Cox process. Furture it specializes to the description of the dependence structure of components of multidimensional subordinators using L'evy copulas. There are examples presented of parametric families of L'evy copulas. On their basis graphs of cross-pair correlation functions, defined analogously to the Cox point process case, are investigated. The work also shows the possibility of simulation of multidimensional subordinators using mentioned families of L'evy copulas. Finally it deals with estimation parameters of Gamma-Ornstein-Uhlenbeck process. It is applied an approach based on Bayes theorem and Markov Chain Monte Carlo method with consequential using of Newton-Raphson algorithm and aproximative likelihood.
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Segment point processes
Honzl, Ondřej ; Beneš, Viktor (referee) ; Pawlas, Zbyněk (advisor)
Naz-ev prace: Bodove proeesy usecek Aut.or: Ondrej Ilonzl Katedra: Katedra. pravdepodobnosti a matematicke statist,iky Vodonci bakalafske praee: RNDr. Zbynek Pawlas, Ph.D. e-mail vedouciho: zbynek.pawlas'O'mfl'.cmn.cz Abstrakt: Prace obsahnje strucny uvod do teoric bodovych procesii na nplnem se- parabilnim lokalne koutpakt iiiiu metrickem prost.oru. Hamcove je ziuinen si>ccii'ilni I>fipad st,acionariiilio ])roc:csu kouipaktiiich ninozin. Dale sc jiran1 vice1 /aincfujo na, Poissonuv prort\ usccek sc /nainyni ro/dcMrnim typickrho /rnu. V roviniirin pfi])aclo pak ukazujc n'i/nr odliady dolkovr int.i'ii/ily I'oissonova jiroccsu usccck, kU're jsou drfinovany na /aklade udaju /iskanych v okuc poxorovani. Hlavnim zajinoin prace st1 stava porovnavani tcclito odhadu die jujich rozpt.ylu. Cilem to- hoto sroviiavani ina byi stanovoni niezc \vlikoHti okna, klcra. fika, dokud jc Icpsi pou/it slozitojsi odhad a odkdy je naopak ro/ninno pouzit odliad. jclioz vvpocot jo snazsi, ale kl.cry pft'ilpoklada., zc inatiie vice iniormaci u po/orovanein JJI'OCCHU. Klicova slova: I'oissonuv i>roces. hodovy proces usccek, odhad delkove intonzit.y Title: Segment point Autlior: Ondrej Ilonzl Deijartuient: DepartiiieiiL ol'Prol)a.l>ilit.y and Mathcinalical Statistics Supervisor: KNDr. Zbyuek Pawlas, Ph.I). Supervisor's (^niail address:...
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