martingale

鞅

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

Translation evidence: Literature usage

Meaning in context

An adapted discrete-time process $M_n$ with $E|M_n|<\infty$ and $E[M_{n+1}\mid\mathcal F_n]=M_n$ almost surely for each $n$, relative to a specified filtration.

对指定信息流适应、每时刻可积，并且下一时刻给定当前信息的条件期望等于当前值的过程。

Example

Partial sums of independent integrable mean-zero increments form a martingale in their natural filtration.

Usage and distinctions

Constant unconditional expectations are insufficient, and enlarging the filtration with future information can destroy the property.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Gregory F. Lawler — Notes on Probability§6.2 Martingales, definition · Checked 2026-10-14

Translation sources

1. 李东风 — 应用随机过程，第6章 鞅（北京大学）§6.1.1 定义，定义6.1 · Checked 2026-10-14

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