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이동평균과정에 대하여
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 이기정 | - |
| dc.contributor.author | 빈무진 | - |
| dc.date.accessioned | 2018-11-08T08:18:53Z | - |
| dc.date.available | 2018-11-08T08:18:53Z | - |
| dc.date.issued | 2015-02 | - |
| dc.identifier.other | 19632 | - |
| dc.identifier.uri | https://dspace.ajou.ac.kr/handle/2018.oak/12779 | - |
| dc.description | 학위논문(석사)--아주대학교 일반대학원 :수학과,2015. 2 | - |
| dc.description.tableofcontents | 1 Introduction 2 Preliminaries 2.1 Conditional expectations 2.2 Reproducing kernel Hilbert spaces 2.3 Wiener processes and It^o stochastic Integral 2.4 The limit set of a sequence of Gaussian processes in C([0; 1]) 3 The Path-regularity of Moving Average Processes 3.1 A moving average process M_x0015__t 3.2 The law of the iterated logarithm and the path-regularity of M_t 3.3 A colored noise process C_x000C__t 4 Geometric Moving Average Processes 4.1 A simple stochastic di_x000B_fferential equation 4.2 Estimation of parameters | - |
| dc.language.iso | eng | - |
| dc.publisher | The Graduate School, Ajou University | - |
| dc.rights | 아주대학교 논문은 저작권에 의해 보호받습니다. | - |
| dc.title | 이동평균과정에 대하여 | - |
| dc.title.alternative | On Moving Average Processes | - |
| dc.type | Thesis | - |
| dc.contributor.affiliation | 아주대학교 일반대학원 | - |
| dc.contributor.alternativeName | Moojin Bin | - |
| dc.contributor.department | 일반대학원 수학과 | - |
| dc.date.awarded | 2015. 2 | - |
| dc.description.degree | Master | - |
| dc.identifier.localId | 695637 | - |
| dc.identifier.url | http://dcoll.ajou.ac.kr:9080/dcollection/jsp/common/DcLoOrgPer.jsp?sItemId=000000019632 | - |
| dc.subject.keyword | 위너과정 | - |
| dc.subject.keyword | 커널 | - |
| dc.description.alternativeAbstract | 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. | - |
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- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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