随笔分类 - Math / Random Process

摘要：1. Definitions Definition 1. We say the process

{X (t), t \geq 0}

$\{X(t),t\ge0\}$ is a continuous-time Markov chain if for all

s, t \geq 0

$s,t\ge0$ and nonnegative integers 阅读全文

posted @ 2023-12-10 11:45 kaleidopink 阅读(45) 评论(0) 推荐(0) 编辑

Markov Chains

摘要：1. Introduction Let

{X_{n}, n = 0, 1, 2, . . .}

$\{X_n,n=0,1,2,...\}$ be a stochastic process that takes on a finite number of possible values. If

X_{n} = i

$X_n=i$ , then the process 阅读全文

posted @ 2023-11-19 16:32 kaleidopink 阅读(126) 评论(0) 推荐(0) 编辑

Poisson Process

摘要：1. Counting process We say that

{N (t), t \geq 0}

$\{N(t),t\ge0\}$ is a counting process if

N (t)

$N(t)$ represents the total number of "events" occur by time

t

$t$ and 阅读全文

posted @ 2023-11-14 17:22 kaleidopink 阅读(27) 评论(0) 推荐(0) 编辑

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