Definition
Let be a probability space with a filtration, for some (totally ordered) index set ; and let be a measurable space. A -valued stochastic process adapted to the filtration is said to possess the Markov property if, for each and each with ,
In the case where is a discrete set with the discrete sigma algebra and, this can be reformulated as follows:
- .
Read more about this topic: Markov Property
Famous quotes containing the word definition:
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)