the integers or the real line. But the concept of stationarity also exists for point processes and random fields, where the index set is not interpreted as time. When the index set can be interpreted as time, a stochastic process is said to be stationary if its finite-dimensional distributions are invariant under translations of time. This type of stochastic process can be used to describe a physical system that is in steady state, but still experiences random fluctuations. The intuition behind stationarity is that as time passes the distribution of the stationary stochastic process remains the same. A sequence of random variables forms a stationary stochastic process only if the random variables are identically distributed. A stochastic process with the above definition of stationarity is sometimes said to be strictly stationary, but there are other forms of stationarity. One example is when a discrete-time or continuous-time stochastic process is said to be stationary in the wide sense, then the process has a finite second moment for all and the covariance of the two random variables and depends only on the number for all . Khinchin introduced the related concept of stationarity in the wide sense, which has other names including covariance stationarity or stationarity in the broad sense. Filtration A filtration is an increasing sequence of sigma-algebras defined in relation to some probability space and an index set that has some total order relation, such as in the case of the index set being some subset of the real numbers. More formally, if a stochastic process has an index set with a total order, then a filtration , on a probability space is a family of sigma-algebras such that for all , where and denotes the total order of the index set . With the concept of a filtration, it is possible to study the amount of information contained in a stochastic process at , which can be interpreted as time . The intuition behind a filtration is that as time passes, more and more information on is known or available, which is captured in , resulting in finer and finer partitions of . Modification A modification of a stochastic process is another stochastic process, which is closely related to the original stochastic process. More precisely, a stochastic process that has the same index set , state space , and probability space as another stochastic process is said to be