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]>

The Fourier analytic approach due to S.M. Berman is considered for a certain class of [alpha]-stable moving average processes, 1 [alpha] = 2. It is proved that the local times of such processes satisfy a uniform Hölder condition of order Q1 - 1/[alpha] logQ1/[alpha] for small intervals Q. A...

We introduce a new generalized family of nonnegative continuous distributions by addingtwo extra parameters to a lifetime distribution, called the baseline distribution, by twice com-pounding a power series distribution. The new family, called the lifetime power series-powerseries family, has a...

We introduce a new generalized family of nonnegative continuous distributions by addingtwo extra parameters to a lifetime distribution, called the baseline distribution, by twice com-pounding a power series distribution. The new family, called the lifetime power series-powerseries family, has a...

The best linear prediction for [alpha]-stable random processes based on some past values is presented. The prediction is the best with respect to a criterion known as stable covariation. The minimum stable covariations can be considered as the smallest error tail probabilities. The predictor...

Recently, Maccheroni et al. [Maccheroni, F., Marinacci, M., 2005. A strong law of large numbers for capacities. Ann. Probab. 33, 1171–1178] have provided an extension of the strong law of large numbers of i.i.d random variables for capacities. In this paper, we formulate new versions of the...

Necessary and sufficient conditions for the existence of order statistics moments of α-stable random variables are introduced. Using the obtained results, all parameters of α-stable distribution are estimated.