랜덤프로세스,random_process

랜덤프로세스,random_process (rev. 1.4)



=random walk?
Related example: 브라운_운동,Brownian_motion

현실을 모델링



Def.
For each outcome $\zeta\in S,$ (ζ: 결과,outcome, S: 표본공간,sample_space)
consider function $X:\zeta\mapsto X(t,\zeta),\quad t\in I$

먼저 결과를(outcome을) 픽스.
then, for fixed $\zeta,$ the graph[1] of function $X(t,\zeta):$

다음은 시간을 픽스.
and for fixed $t=t_k,\;X(t_k,\forall\zeta)=X_k$ : random variable

then, $\lbrace X(t,\forall\zeta\in S),t\in I\rbrace\equiv X(t),\quad t\in I$
⇔ random process, r.p., 확률과정

여기서 만약 $I$ 가
countable set이면, $X(t)$ 는 discrete-time r.p. (이산시간확률과정)
continuous set이면, $X(t)$ 는 continuous-time r.p. (연속시간확률과정)

from http://www.kocw.net/home/search/kemView.do?kemId=1279832 22. Random process 1:11

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  • [1] 이 그래프는 이름이 여러가지임. sample path(표본경로), sample function(표본함수), realization of random process(확률 과정의 실현)