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→Definitions定义
so the law of a <math>X</math> can be written as:
so the law of a <math>X</math> can be written as:
所以 a 的定律可以写成:
所以 <math>X</math>的定律可以写成:
A stochastic process is defined as a collection of random variables defined on a common [[probability space]] <math>(\Omega, \mathcal{F}, P)</math>, where <math>\Omega</math> is a [[sample space]], <math>\mathcal{F}</math> is a <math>\sigma</math>-[[Sigma-algebra|algebra]], and <math>P</math> is a [[probability measure]]; and the random variables, indexed by some set <math>T</math>, all take values in the same mathematical space <math>S</math>, which must be [[measurable]] with respect to some <math>\sigma</math>-algebra <math>\Sigma</math>.<ref name="Lamperti1977page1"/>
A stochastic process is defined as a collection of random variables defined on a common [[probability space]] <math>(\Omega, \mathcal{F}, P)</math>, where <math>\Omega</math> is a [[sample space]], <math>\mathcal{F}</math> is a <math>\sigma</math>-[[Sigma-algebra|algebra]], and <math>P</math> is a [[probability measure]]; and the random variables, indexed by some set <math>T</math>, all take values in the same mathematical space <math>S</math>, which must be [[measurable]] with respect to some <math>\sigma</math>-algebra <math>\Sigma</math>.<ref name="Lamperti1977page1"/>
随机过程被定义为在一个公共[[概率空间]]<math>（\Omega，\mathcal{F}，P）</math>上定义的随机变量集合，其中<math>\Omega</math>是[[样本空间]]，<math>\mathcal{F}</math>是一个<math>\sigma</math>-[[sigma代数|代数]]，<math>P</math>是[[概率测度]]；而随机变量，由某个集合<math>T</math>索引，所有值都取同一个数学空间<math>S</math>，对于某些<math>\sigma</math>-代数<math>\sigma</math><ref name=“Lamperti1977page1”/>
随机过程被定义为在一个公共[[概率空间]]<math>(\Omega, \mathcal{F}, P)</math>上定义的随机变量集合，其中<math>\Omega</math> 是[[样本空间]]，<math>\mathcal{F}</math>是一个<math>\sigma</math>-[[sigma代数|代数]]，<math>P</math>是[[概率测度]]；而随机变量，由某个集合<math>T</math>索引，所有值都取同一个数学空间<math>S</math>，对于某些<math>\sigma</math>-代数<math>\sigma</math><ref name=“Lamperti1977page1”/>
For a stochastic process <math>X</math> with law <math>\mu</math>, its finite-dimensional distributions are defined as:
For a stochastic process <math>X</math> with law <math>\mu</math>, its finite-dimensional distributions are defined as: