更改

它们都有相同的[[概率分布]]。平稳随机过程的指标集通常被解释为时间，因此可以是整数或实线。<ref name="Lamperti1977page6">{{cite book|author=John Lamperti|title=Stochastic processes: a survey of the mathematical theory|url=https://books.google.com/books?id=Pd4cvgAACAAJ|year=1977|publisher=Springer-Verlag|isbn=978-3-540-90275-1|pages=6 and 7}}</ref><ref name="GikhmanSkorokhod1969page4">{{cite book|author1=Iosif I. Gikhman |author2=Anatoly Vladimirovich Skorokhod|title=Introduction to the Theory of Random Processes|url=https://books.google.com/books?id=yJyLzG7N7r8C&pg=PR2|year=1969|publisher=Courier Corporation|isbn=978-0-486-69387-3|page=4}}</ref> But the concept of stationarity also exists for point processes and random fields, where the index set is not interpreted as time.<ref name="Lamperti1977page6"/><ref name="Adler2010page14">{{cite book|author=Robert J. Adler|title=The Geometry of Random Fields|url=https://books.google.com/books?id=ryejJmJAj28C&pg=PA263|year=2010|publisher=SIAM|isbn=978-0-89871-693-1|pages=14, 15}}</ref><ref name="ChiuStoyan2013page112">{{cite book|author1=Sung Nok Chiu|author2=Dietrich Stoyan|author3=Wilfrid S. Kendall|author4=Joseph Mecke|title=Stochastic Geometry and Its Applications|url=https://books.google.com/books?id=825NfM6Nc-EC|year=2013|publisher=John Wiley & Sons|isbn=978-1-118-65825-3|page=112}}</ref>

它们都有相同的[[概率分布]]。平稳随机过程的指标集通常被解释为时间，因此可以是整数或实线。<ref name="Lamperti1977page6">{{cite book|author=John Lamperti|title=Stochastic processes: a survey of the mathematical theory|url=https://books.google.com/books?id=Pd4cvgAACAAJ|year=1977|publisher=Springer-Verlag|isbn=978-3-540-90275-1|pages=6 and 7}}</ref><ref name="GikhmanSkorokhod1969page4">{{cite book|author1=Iosif I. Gikhman |author2=Anatoly Vladimirovich Skorokhod|title=Introduction to the Theory of Random Processes|url=https://books.google.com/books?id=yJyLzG7N7r8C&pg=PR2|year=1969|publisher=Courier Corporation|isbn=978-0-486-69387-3|page=4}}</ref> 但对于点过程和随机场也存在平稳性的概念，其中指标集不被解释为时间。<ref name="Lamperti1977page6"/><ref name="Adler2010page14">{{cite book|author=Robert J. Adler|title=The Geometry of Random Fields|url=https://books.google.com/books?id=ryejJmJAj28C&pg=PA263|year=2010|publisher=SIAM|isbn=978-0-89871-693-1|pages=14, 15}}</ref><ref name="ChiuStoyan2013page112">{{cite book|author1=Sung Nok Chiu|author2=Dietrich Stoyan|author3=Wilfrid S. Kendall|author4=Joseph Mecke|title=Stochastic Geometry and Its Applications|url=https://books.google.com/books?id=825NfM6Nc-EC|year=2013|publisher=John Wiley & Sons|isbn=978-1-118-65825-3|page=112}}</ref>

具有上述平稳性定义的随机过程有时被称为严格平稳的，但也有其他形式的平稳性。一个例子是当离散时间或连续时间随机过程<math>X</math>被称为广义平稳时，那么，对于t</math>中的所有<math>t\n，过程<math>X</math>有一个有限的第二时刻，两个随机变量的协方差只取决于t</math>中所有<math>t\t\的数<math>h</math><ref name="Doob1990page94"/><ref name="Florescu2014page298">{{cite book|author=Ionut Florescu|title=Probability and Stochastic Processes|url=https://books.google.com/books?id=Z5xEBQAAQBAJ&pg=PR22|year=2014|publisher=John Wiley & Sons|isbn=978-1-118-59320-2|pages=298, 299}}</ref> [[Aleksandr Khinchin | Khinchin]]介绍了“广义平稳性”的相关概念，其他名称包括“协方差平稳性”或“广义平稳性”。<ref name="Florescu2014page298"/><ref name="GikhmanSkorokhod1969page8">{{cite book|author1=Iosif Ilyich Gikhman|author2=Anatoly Vladimirovich Skorokhod|title=Introduction to the Theory of Random Processes|url=https://books.google.com/books?id=yJyLzG7N7r8C&pg=PR2|year=1969|publisher=Courier Corporation|isbn=978-0-486-69387-3|page=8}}</ref>

具有上述平稳性定义的随机过程有时被称为严格平稳的，但也有其他形式的平稳性。一个例子是当离散时间或连续时间随机过程<math>X</math>被称为广义平稳时，那么这个过程<math>X</math>，有一个有限的第二时刻对于所有<math>t\in T</math>和两个随机变量的协方差 <math>X_t</math> 和 <math>X_{t+h}</math> 只取决于在<math>t\in T</math>时的数值<math>h</math><ref name="Doob1990page94"/><ref name="Florescu2014page298">{{cite book|author=Ionut Florescu|title=Probability and Stochastic Processes|url=https://books.google.com/books?id=Z5xEBQAAQBAJ&pg=PR22|year=2014|publisher=John Wiley & Sons|isbn=978-1-118-59320-2|pages=298, 299}}</ref> [[Aleksandr Khinchin | Khinchin]]介绍了“广义平稳性”的相关概念，其他名称包括“协方差平稳性”或“广义平稳性”。<ref name="Florescu2014page298"/><ref name="GikhmanSkorokhod1969page8">{{cite book|author1=Iosif Ilyich Gikhman|author2=Anatoly Vladimirovich Skorokhod|title=Introduction to the Theory of Random Processes|url=https://books.google.com/books?id=yJyLzG7N7r8C&pg=PR2|year=1969|publisher=Courier Corporation|isbn=978-0-486-69387-3|page=8}}</ref>

====过滤 Filtration====

====过滤 Filtration====