General stability for stochastic pantograph delay evolution equations driven by tempered fractional noise with Hurst index H ∈ (0, 1/2) ∪ (1/2, 1)

A theoretical framework for general stability is established in this paper for stochastic pantograph delay evolution equations driven by tempered fractional Brownian motion (tfBm) with Hurst index [Formula: see text] and tempered parameter [Formula: see text]. A novel estimate of the stochastic integral with respect to tfBm is the key of our analyses, being valid for both [Formula: see text] and [Formula: see text]. We prove the global existence, mean square stability with general decay rate and global Hölder regularity in time of the mild solution by utilizing the convolution method, the Young convolution inequality, the semigroup theory and the Banach fixed point theorem. These stabilities may be specialized as the exponential, polynomial, and logarithmic one.