Bessel-like processes and SDE

Bessel and Volatility-Stabilized Processes

Bessel and Volatility-Stabilized Processes

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...

SDE decomposition and A-type stochastic interpretation in nonequilibrium processes

A Piecewise Linear Sde Driven by a Lévy Processes

We consider an SDE with piece-wise linear drift driven by a spectrally onesided Lévy process. We show this SDE has some connections with queueing and storage models and apply this to obtain the invariant distribution.

type SDE approach to positive self - Similar Markov processes ∗

We present a new approach to positive self-similar Markov processes (pssMps) by reformulating Lamperti’s transformation via jump type SDEs. As applications, we give direct constructions of pssMps (re)started continuously at zero if the Lamperti transformed Lévy process is spectrally negative. Our paper can be seen as a continuation of similar studies for continuous state branching processes.