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- W2083571412 abstract "Motivated by the central limit theorem for weakly dependent variables, we show that the Brownian motion {X(t);t∈[0,1]}, can be modeled as a process with independent increments, satisfying the following limiting condition.liminfh↓0Ef(h-1/2[X(s+h)-X(s)])⩾Ef(X(1))almost surely for all 0⩽s<1, where Ef(X(1))<∞ and f:R→R is a symmetric, continuous, convex function with f(0)=0, strictly increasing on R+ and satisfying the following growth condition:f(Kx)⩽Kpf(x),for a certainp∈[1,2), all K⩾K0 and all x>0(for example, f(x)=xp[A+Bln(1+Cx)], with x>0, p∈[1,2), A>0 and B,C⩾0)." @default.
- W2083571412 created "2016-06-24" @default.
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- W2083571412 date "2006-02-01" @default.
- W2083571412 modified "2023-09-26" @default.
- W2083571412 title "Another approach to Brownian motion" @default.
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- W2083571412 doi "https://doi.org/10.1016/j.spa.2005.09.004" @default.
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