Realized Power Variation of some Fractional Stochastic Integrals
Laws of Large Numbers and Central Limit Theorems
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This thesis is concerned with the realized power variation of certain classes of stochastic processes. The author considers fractional stochastic integrals, i.e., stochastic integrals with respect to fractional Brownian Motion, and presents results on the asymptotic behaviour of the realized power variation of these processes. Outlooks on more general results that apply for a class of functionals that contains the realized power variation, as well as results on the realized power variation of integrated stable processes (instead of fractional stochastic integrals) are provided. The work is aim...
This thesis is concerned with the realized power variation of certain classes of stochastic processes. The author considers fractional stochastic integrals, i.e., stochastic integrals with respect to fractional Brownian Motion, and presents results on the asymptotic behaviour of the realized power variation of these processes. Outlooks on more general results that apply for a class of functionals that contains the realized power variation, as well as results on the realized power variation of integrated stable processes (instead of fractional stochastic integrals) are provided. The work is aimed at students and mathematicians working in the field of probability and statistics as well as practitioners, especially in the finance area.
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