Learning Notes

Stochastic – Incremental Process

Independent Incremental Process

For a stochastic process X_T with sample space t_1, t_2, \dots, t_n \in T such that t_1 < t_2 < \dots < t_n then

\displaystyle X_{t2} - X_{t1} , X_{t3} - X_{t2} , \dots , X_{tn} - X_{tn-1}

are independent.

Stationary Independent Incremental Process

For an independent incremental process X_T , it is said to be stationary if it satisfy:

\displaystyle \{X_{t_i + h} - X_{t_{i-1} + h}\} = \{X_{t_i} - X_{t_{i-1}}\}

A stationary independent incremental process is also called Levy Process

 

See Also

Stochastic Process
Stationary Process – Stochastic
Ergodic Process – Stochastic

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