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Estimates of Extremes of Random Functions by Finite Dimensional (FD) Models
Estimates of Extremes of Random Functions by Finite Dimensional (FD) Models
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211152139
- ISBN
- 9798384051367
- DDC
- 519
- 저자명
- Xu, Hui.
- 서명/저자
- Estimates of Extremes of Random Functions by Finite Dimensional (FD) Models
- 발행사항
- [Sl] : Cornell University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 168 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
- 주기사항
- Advisor: Grigoriu, Mircea.
- 학위논문주기
- Thesis (Ph.D.)--Cornell University, 2024.
- 초록/해제
- 요약Most stochastic problems do not admit analytical solutions. Numerical methods can only solve problems involving finite sets of random variables. For example, these methods cannot deliver the distribution of the extreme supt∈[0,τ] |X(t)| of a real-valued, continuous-time stochastic process X(t) since these processes are uncountable families of random variables indexed by time. Numerical methods can only deliver estimates of extremes supt∈[0,τ] |Xd(t)| of finite dimensional (FD) surrogates Xd(t) of X(t), i.e., deterministic functions of time and d random variables. These numerical solutions are useful only if the distribution of supt∈[0,τ] |Xd(t)| converges to that of supt∈[0,τ] |X(t)| as d, referred to as stochastic dimension, increases to infinity.We develop conditions under which the distributions of functionals of Xd(t) converge to those of functionals of target process X(t), where X(t) can be a real/vector-valued Gaussian/non-Gaussian process denoting the input to or the output of dynamical systems. Under these conditions, the distributions of extremes of FD processes can be used as surrogates for those of target processes provided that the stochastic dimension d is sufficiently large. These theoretical results are illustrated by numerical examples which show consistency with theoretical developments.
- 일반주제명
- Applied mathematics
- 일반주제명
- Theoretical mathematics
- 일반주제명
- Mathematics
- 키워드
- Finite sets
- 기타저자
- Cornell University Applied Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798384051367
■035 ▼a(MiAaPQ)AAI31484688
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a519
■1001 ▼aXu, Hui.▼0(orcid)0000-0001-8463-469X
■24510▼aEstimates of Extremes of Random Functions by Finite Dimensional (FD) Models
■260 ▼a[Sl]▼bCornell University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a168 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-03, Section: B.
■500 ▼aAdvisor: Grigoriu, Mircea.
■5021 ▼aThesis (Ph.D.)--Cornell University, 2024.
■520 ▼aMost stochastic problems do not admit analytical solutions. Numerical methods can only solve problems involving finite sets of random variables. For example, these methods cannot deliver the distribution of the extreme supt∈[0,τ] |X(t)| of a real-valued, continuous-time stochastic process X(t) since these processes are uncountable families of random variables indexed by time. Numerical methods can only deliver estimates of extremes supt∈[0,τ] |Xd(t)| of finite dimensional (FD) surrogates Xd(t) of X(t), i.e., deterministic functions of time and d random variables. These numerical solutions are useful only if the distribution of supt∈[0,τ] |Xd(t)| converges to that of supt∈[0,τ] |X(t)| as d, referred to as stochastic dimension, increases to infinity.We develop conditions under which the distributions of functionals of Xd(t) converge to those of functionals of target process X(t), where X(t) can be a real/vector-valued Gaussian/non-Gaussian process denoting the input to or the output of dynamical systems. Under these conditions, the distributions of extremes of FD processes can be used as surrogates for those of target processes provided that the stochastic dimension d is sufficiently large. These theoretical results are illustrated by numerical examples which show consistency with theoretical developments.
■590 ▼aSchool code: 0058.
■650 4▼aApplied mathematics
■650 4▼aTheoretical mathematics
■650 4▼aMathematics
■653 ▼aNumerical methods
■653 ▼aDynamical systems
■653 ▼aFinite sets
■690 ▼a0364
■690 ▼a0642
■690 ▼a0405
■71020▼aCornell University▼bApplied Mathematics.
■7730 ▼tDissertations Abstracts International▼g86-03B.
■790 ▼a0058
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17163141▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
