First Order Markov Process

A First Order Markov Process is a Markov process where the probabilities for choosing the next event depend only on the immediately preceding event.

• • …
• Counter-Example(s):
  • a Second Order Markov Process.
  • a Zero Order Markov Process.
• See: Markov Model, Markov Property.

---

---

References

2009

• …
  • First Order Markov Process: Let {X1,X2,…,Xn} be a sequence of random variables (or vectors), e.g. the joint angle vectors in a gait cycle over a period of time. We call this process is a first order Markov process if the following Markov property is true:

2003

• http://www.moz.ac.at/sem/lehre/lib/bib/software/cm/Notes_from_the_Metalevel/markov.html
  • QUOTE: … In a Markov process past events represent a state, or context, for determining the probabilities of subsequent events. The number of past events used by the process is called its order. In a first order process the probabilities for choosing the next event depend only on the immediately preceding event. In a second order Markov process the probabilities for the next choice depend on the last two events. A Markov process can reflect any number of past choices, including the degenerate case of no past choices. A zero order Markov Process is equivalent to weighted random selection. …

---