论文信息 - Maximal inequalities for the Ornstein-Uhlenbeck process

Maximal inequalities for the Ornstein-Uhlenbeck process

Consider the random movement of a Brownian particle suspended in a liquid. The EinsteinSmoluchowski theory suggests the standard Brownian motion Bt N(0; t) as a model for the position of the particle. The Ornstein-Uhlenbeck theory [6] relies upon Newtonian mechanics and suggests that the position of the Brownian particle should be modelled as Xt = R t 0 Vr dr where Vt = e t R t 0 e dBr N(0; 1 2 (1 e 2 t)) is the Brownian velocity solving the Langevin equation:

Goran Peskir | S. Graversen | G. Peskir | S. E. Graversen

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