26 research outputs found
Stein approximation for functionals of independent random sequences
We derive Stein approximation bounds for functionals of uniform random
variables, using chaos expansions and the Clark-Ocone representation formula
combined with derivation and finite difference operators. This approach covers
sums and functionals of both continuous and discrete independent random
variables. For random variables admitting a continuous density, it recovers
classical distance bounds based on absolute third moments, with better and
explicit constants. We also apply this method to multiple stochastic integrals
that can be used to represent U-statistics, and include linear and quadratic
functionals as particular cases
Supremum distribution of Bessel process of drifting Brownian motion
Let (B^{(1)}_t ;B^{(2)}_t ;B^{(3)}_t + \mu t) be a three-dimensional Brownian
motion with drift \mu, starting at the origin. Then X_t = ||(B^{(1)}_t
;B^{(2)}_t ;B^{(3)}_t +\mu t)||, its distance from the starting point, is a
diffusion with many applications. We investigate the distribution of the
supremum of (X_t), give an infinite-series formula for its density and an exact
estimate by elementary functions