stochastic process

随机过程

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

Translation evidence: Literature usage

Meaning in context

An indexed family (Xt)t∈T(X_t)_{t\in T} of random variables or random elements on one probability space, with a specified common state space.

同一概率空间上按指标集合排列、取值于指定状态空间的一族随机变量或随机元素。

Example

Independent coin increments (ξn)n≥1(\xi_n)_{n\ge1} form a discrete-time process; Brownian motion has continuous time.

Usage and distinctions

The time index and the state space can be discrete or continuous independently; an arbitrary process need not have continuous paths.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

  1. Gregory F. Lawler — Notes on ProbabilitySection 7, Brownian motion, opening fixed-time and fixed-outcome interpretation · Checked 2026-10-14

Translation sources

  1. 李东风 — 应用随机过程，第7章 布朗运动（北京大学）§7.1.3 高斯过程，定义7.2中“随机过程”用语 · Checked 2026-10-14
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