Stochastic Process with Independent Increments

Topics: Types of Stochastic Processes

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(definition)

A stochastic process with independent increments is a stochastic process where, for any $0<t_1<t_2<\cdots <t_n$ parameters, the variables $X_{t_1},X_{t_2}-X_{t_1},X_{t_3}-X_{t_2},\dots ,X_{t_n}-X_{t_{n-1}}$ are independent.

Examples of stochastic processes with independent increments include homogeneous Poisson processes.