Strong Approximation of Bessel Processes

Strong approximation of stochastic processes using random walks

Some Processes Associated with Fractional Bessel Processes

Let B = {(B1 t , . . . , Bd t ) , t ≥ 0} be a d-dimensional fractional Brownian motion with Hurst parameter H and let Rt = √ (B1 t ) 2 + · · · + (Bd t )2 be the fractional Bessel process. Itô’s formula for the fractional Brownian motion leads to the equation Rt = ∑d i=1 ∫ t 0 Bi s Rs dBi s + H(d − 1) ∫ t 0 s2H−1 Rs ds . In the Brownian motion case (H = 1/2), Xt = ∑d i=1 ∫ t 0 Bi s Rs dBi s is a...

Bessel and Volatility-Stabilized Processes

Bessel and Volatility-Stabilized Processes

Approximation of Bessel Beams with Annular Arrays

1 Abstract — It is shown that the limited-diffraction Bessel beam of order zero can be generated by a transducer with equal-area division of elements and with a fixed prefocus, i.e. conventional transducers used in medical imaging equipment. The element division implies that the scaling parameter must be chosen to contain the first lobe of the Bessel function in the first element. In addition t...

STRONG APPROXIMATION OF THE QUANTILE PROCESSES AND ITS APPLICATIONS UNDER STRONG MIXING PROPERTIES by

Given some regularity conditions on the distribution F(.) of a random sample X h ..., Xn emanating from a strictly stationary sequence of random variables satisfying a strong mixing condition, it is shown that the sequence of quantile processes {n1hf(F1(s))(F;1(s)-F1(s)); 0 < s < I} behaves like a sequence of Brownian bridges {BD(s); 0 < s < I}. The latter is then utilized to construct (i) simu...