It is a process where sustained increases in non-overlapping time intervals, are independent random variables. So given the time:


The random variables, equal to the increases of the process Y:


are independent.

When the increments suffered in intervals of equal length, are equally distributed, the process is called homogeneous with independent increments.

Bibliography
AA.VV., Matematica Finanziaria, Monduzzi Editore, 1998
GRINSTEAD M. C. and SNELL J. L., Introduction to Probability, American Mathematical Society, 1997

Editor: Giuliano DI TOMMASO