Can someone be kind enough to explain what "independent increment" is? Please, easy explanation. I browsed thru different websites (inc wiki) but couldn't get an explanation that was clear and/or easy enough for me to understand.
Thank you!!
Can someone be kind enough to explain what "independent increment" is? Please, easy explanation. I browsed thru different websites (inc wiki) but couldn't get an explanation that was clear and/or easy enough for me to understand.
Thank you!!
For a time interval $T$ equipped with a linear order $\leq$, a stochastic process $X$ - say a real valued one - indexed by $T$ is said to have independent increments, if for times $s_1 < t_1 \leq s_2 < t_2 \leq \ldots \leq s_d < t_d$ the random variables $X_{t_1} - X_{s_1}, \ldots, X_{t_d} - X_{s_d}$ are independent.