On local fluctuations of stable moving average processes

Let X(t) = [is proportional to]t-[infinity]f(t-s) dZ(s) be a symmetric stable moving average process of index [alpha], 1 < [alpha] [less-than-or-equals, slant] 2. It is proved that when f has a jump discontinuity at a point or when f(x) --> 0 slowly as x [downwards arrow] 0, then almost every sample function of X(t), , is a Janik (J1) function with infinite [gamma]-variation, [gamma][set membership, variant][1, [alpha]).