Abstract
In this paper we study the grey Brownian motion, namely its representation and local time. First it is shown that grey Brownian motion may be represented in terms of a standard Brownian motion and then using a criterium of S. Berman, Trans. Amer. Math. Soc., 137, 277–299 (1969), we show that grey Brownian motion admits a λ-square integrable local time almost surely (λ denotes the Lebesgue measure). As a consequence we obtain the occupation formula and state possible generalizations of these results.
Highlights
Grey Brownian motion was introduced by W
Schneider[1, 2] as a model for slow anomalous diffusions, i.e., the marginal density function of the Grey Brownian motion (gBm) is the fundamental solution of the time-fractional diffusion equation, see Ref. 3
In this paper we investigate the class of gBm, namely their representation in terms of standard Brownian motion (Bm) and show the existence of local time
Summary
In this paper we study the grey Brownian motion, namely its representation and local time. First it is shown that grey Brownian motion may be represented in terms of a standard Brownian motion and using a criterium of S. Soc., 137, 277–299 (1969), we show that grey Brownian motion admits a λ-square integrable local time almost surely (λ denotes the Lebesgue measure). As a consequence we obtain the occupation formula and state possible generalizations of these results
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