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7
Stochastic or Random
Processes and Time Series
7.1 STOCHASTIC PROCESSES AND TIME SERIES: BASICS
A stochastic or random process is a sequence of random variables X(t) with a distribution that may
vary with time t and a joint distribution for the entire sequence. For example, a Gaussian process is a
sequence of normally distributed variables with a joint distribution that is also normal. The process
is stationary if the distribution is constant with time t. To be less restrictive, we can make a weaker
statement considering the process stationary if the mean and variance are constant. For example, a
Gaussian process dened by identical independent ...