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We present a general method for constructing stochastic processes withprescribed local form. Such processes include variable amplitudemultifractional Brownian motion, multifractional $\alpha$-stable processes, andmultistable processes, that is processes that are locally $\alpha(t)$-stablebut where the stability index $\alpha(t)$ varies with $t$. In particular weconstruct multifractional multistable processes where both the localself-similarity and stability indices vary.

Multifractional, multistable, and other processes with prescribed local form