Abstract
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  1 Jan 2010 
Place of Publication  Ithaca 
Publisher  
Publication status  Published  2010 
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Some convergence results on stable infinite moving average processes and stable selfsimilar processes. / Can, S.U.
Ithaca : Cornell university, 2010. 104 p.Research output: Thesis › Phd Thesis 4 Research NOT TU/e / Graduation NOT TU/e)
TY  THES
T1  Some convergence results on stable infinite moving average processes and stable selfsimilar processes
AU  Can, S.U.
PY  2010
Y1  2010
N2  NonGaussian stable stochastic models have attracted growing interest in recent years, due to their connections to limit theorems and due to empirical evidence pointing to heavierthanGaussian probability tails in many natural situations. We study the structure of two broad classes of stable stochastic processes through some convergence results. In the first half of the thesis, we study the integrated periodogram for discretetime infinite moving average processes with i.i.d. stable noise. We show that for such processes, a collection of weighted integrals of the periodogram, considered as a functionindexed stochastic process, converges weakly to a limit which can be represented as an infinite Fourier series with i.i.d. stable coefficients. The convergence works under certain assumptions on the Fourier coefficients of the index functions. We also extend the weak convergence results to stochastic volatility processes with stable noise, which are of interest in financial time series analysis. In the second half, we describe a family of continuoustime stable processes with stationary increments that are asymptotically or exactly selfsimilar. We show that they arise naturally as a large time scale limit in a situation where many users perform independent random walks and collect heavytailed random rewards depending on their position on the integer line. We study various properties of the limiting process. This work generalizes an earlier construction by Cohen and Samorodnitsky (2006).
AB  NonGaussian stable stochastic models have attracted growing interest in recent years, due to their connections to limit theorems and due to empirical evidence pointing to heavierthanGaussian probability tails in many natural situations. We study the structure of two broad classes of stable stochastic processes through some convergence results. In the first half of the thesis, we study the integrated periodogram for discretetime infinite moving average processes with i.i.d. stable noise. We show that for such processes, a collection of weighted integrals of the periodogram, considered as a functionindexed stochastic process, converges weakly to a limit which can be represented as an infinite Fourier series with i.i.d. stable coefficients. The convergence works under certain assumptions on the Fourier coefficients of the index functions. We also extend the weak convergence results to stochastic volatility processes with stable noise, which are of interest in financial time series analysis. In the second half, we describe a family of continuoustime stable processes with stationary increments that are asymptotically or exactly selfsimilar. We show that they arise naturally as a large time scale limit in a situation where many users perform independent random walks and collect heavytailed random rewards depending on their position on the integer line. We study various properties of the limiting process. This work generalizes an earlier construction by Cohen and Samorodnitsky (2006).
M3  Phd Thesis 4 Research NOT TU/e / Graduation NOT TU/e)
PB  Cornell university
CY  Ithaca
ER 