Module 3:Branching process, Application of Markov chains, Markov Processes with discrete and                 continuous state space
  Lecture 12:Weiner Process
 

 

Note

  • For large values of ,



  •  and  are mutually independent, which implies  is a Markov process

Thus we say a stochastic process is Weiner-Einsten process (Figure 3.2) with drift parameter  and variance parameter  if

1. For disjoint intervals  and  where ,  and  are independent and this implies it is Markov process with independent increments (Figure 3.2).

Figure 3.2: Illustration of Weiner-Einsten process to show that it has independent increments

2.  and this implies it is Gaussian.

3. Since # 2 above is true hence the transition probability density function is given by