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A note on $α$-IDT processes

In this note, we introduce the notion of $α$-IDT processes which is obtained from a slight and fundamental modification of the IDT property. Several examples of $α$-IDT processes are given and Gaussian processes which are $α$-IDT are characterized. A kind example of this Gaussian $α$-IDT is the standard fractional Brownian motion. Also, we invest some links between the $α$-IDT property, with selfdecomposability, temporal selfdecomposability, stability and self similarity.