Representation of self-similar Gaussian processes

Abstract

a b s t r a c tWe develop the canonical Volterra representation for a self-similar Gaussian process by using the Lamperti transformation of the corresponding stationary Gaussian process, where this latter one admits a canonical integral representation under the assumption of pure non-determinism. We apply the representation obtained to the equivalence in law for self-similar Gaussian processes.

Necessary and sufficient conditions for Hölder continuity of Gaussian processes

“…Then X is purely non-deterministic if H X 0+ is trivial. By [11] a purely non-deterministic Gaussian self-similar process admits the representation…”

Pathwise asymptotics for Volterra processes conditioned to a noisy version of the Brownian motion

“…whereῩ is defined in (21) SinceῩ is the covariance function of a continuous Volterra process, a large deviation principle for 1] ) ε>0 actually holds from Theorem 2 with the inverse speed γ 2 ε and the good rate function given by (22). From Equation (18) and Remark 2 the same large deviation principle holds for the noncentered family…”

Path Properties of a Generalized Fractional Brownian Motion

“…Consider X(t) = t 0 κ(t, u)B(du) , t ≥ 0 with a Volterra kernel κ(t, u) = (t − u) α u −γ/2 . This process or similar processes have been recently studied by Yazigi (2015) [23]. By Theorem 2.1 in [23], the Volterra kernel κ can be written as…”

“…This process or similar processes have been recently studied by Yazigi (2015) [23]. By Theorem 2.1 in [23], the Volterra kernel κ can be written as…”