Στοχαστικές διαδικασίες με υπο συνθήκη στάσιμες και ανεξάρτητες προσαυξήσεις και εφαρμογές
Stochastic processes with conditionally independent and stationary increments and applications
KeywordsΣτοχαστικές διαδικασίες ; Θεωρία κινδύνου ; Νόμοι 0-1 ; Υπό συνθήκη διαδιασίες ; Νόμοι των Μεγάλων Αριθμών
In the present thesis the class of stochastic processes with conditionally independent and stationary increments is examined. Special cases of these processes consist the mixed Poisson stochastic processes, the Cox processes and the conditionally Wiener stochastic processes. These processes are equivalent to random time transformations of processes with independent stationary increments where the time process is independent of the original process. Basic properties and several limit theorems, including 0-1 Laws, weak and strong Laws of Large Numbers of the above processes are proven. As applications some examples, including an interesting example of a conditional Wiener process as a model for depicting the Brownian motion of a particle in a liquid medium are presented. Mixed Poisson processes and conditional Wiener processes ar applied to Risk Theory and to the stock prices' modelling. In order to achieve a systematic study of the above mentioned processes, a number of results related to the Laws 0-1, the Laws of Large Numbers and the derived processes, which presented in previous chapters, are required.