Random sampling of continuous objects : can we computably generate brownian motions? = 브라운 운동을 포함한 연속적 객체 확률추출의 계산가능성can we computably generate brownian motions?

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Randomization is a very powerful tool which can reduce the complexity of a lot of algorithms in practice. However, to implement a randomized algorithm, sampling procedure from the fixed probability distribution is essential. In this paper, we formalized the sampling procedure from continuous probability distribution in the sense of Type-2 Theory of Effectivity which is theoretical framework to handle the computation over continuous data. We first show that every Borel probability measure on second countable $T_0$ spaces is just a push-forward measure of Canonical probability measure on Cantor Space. This is the extension of the result by Simpson and Schr$\ddot{o}$der, 2006. Second result is concerned with Brownian motion as the probability measure on the space of continuous function $f$ :[0,1]-> $\mathbb{R}$ with $f$(0)=0. We figure out the condition when such a measure can be sampled. This measure can be sampled if and only if its family of modulus of continuity can be sampled.
Advisors
Ziegler, Martinresearcher마틴 지글러researcher
Description
한국과학기술원 :전산학부,
Publisher
한국과학기술원
Issue Date
2020
Identifier
325007
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 전산학부, 2020.2,[iii, 17 p. :]

Keywords

Computable Analysis▼aType-2 Theory of Effectivity▼aRandom sampling▼aProbability Theory▼aRandom Variable▼aWiener Process▼aBrownian motion; 계산 해석학▼a유형-2 계산이론▼a확률추출▼a확률론▼a확률변수▼a위너 확률과정▼a브라운 운동

URI
http://hdl.handle.net/10203/284675
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=911006&flag=dissertation
Appears in Collection
CS-Theses_Master(석사논문)
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