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이동평균과정에 대하여
- Alternative Title
- On Moving Average Processes
- Author(s)
- 빈무진
- Alternative Author(s)
- Moojin Bin
- Advisor
- 이기정
- Department
- 일반대학원 수학과
- Publisher
- The Graduate School, Ajou University
- Publication Year
- 2015-02
- Language
- eng
- Alternative Abstract
- In this thesis we consider Gaussian moving average processes X(t) which have the form X(t)=_int_0^t \phi(t-s)dw_s, where w_t is a Wiener process. Especially, we are interested in two cases \phi_1(x)=\mathbbm{1}_[0,a](x) +\mathbbm{1}_(a,1)(x) and \phi_2(x)=x^\beta. We shall call φ the kernel of the process. The motivation of this consideration lies on the dependence of increments of a random process. The increments of a Wiener process are independent, hence when we build a model with it, we assume that the increments of model are uncorrelated. However, it seems far from reality when we need a stochastic process with correlated (positively or negatively) increments. We will see that the random process M_t having \phi_1 as the kernel shares many properties with a Wiener process but it has positively dependent increments. This process is a toy model of the random process C_t which has \phi_2 as the kernel. C_t can be understood as a fractional integration of order \beta+1 of white noise. We study properties of C_t. As an application, we consider a stochastic di_x000B_fferential equation involving M_t and discuss how to fi_x000C_nd parameters of M_t from sampling.
- Fulltext
- Appears in Collections:
- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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