Poisson process

泊松过程

Probability · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

For rate $\lambda>0$, a right-continuous counting process $N_t$ starting at zero with stationary independent increments and $N_t-N_s\sim\operatorname{Pois}(\lambda(t-s))$ for $s<t$.

从0出发、右连续的计数过程，不相交区间增量独立，s至t的计数增量服从参数λ(t−s)的泊松分布。

Example

For rate $3$, the probability of no arrival in two time units is $e^{-6}$.

Usage and distinctions

A Poisson random variable describes one count; a Poisson process specifies the joint evolution of counts.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Gregory F. Lawler — Stochastic Calculus: An Introduction with Applications§6.2 Poisson process, counting construction and rate · Checked 2026-10-14

Translation sources

1. 李东风 — 应用随机过程，第3章 泊松过程（北京大学）§3.1 泊松过程定义，定义3.1–3.2 · Checked 2026-10-14

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.