Convergent multiplicative processes repelled from zero: power laws and truncated power laws

Rama Cont, Didier Sornette

Random multiplicative processes $w_t={\lambda }_1{\lambda }_2...{\lambda }_t$ (with < λ_j > 0 ) lead, in the presence of a boundary constraint, to a distribution $P(w_t)$ in the form of a power law $w_t^…