Random fields and central limit theorem in some generalized Hölder spaces (Q2769704)

Consider a random field \(\psi= \{\psi(t),\;t\in T\}\), \(T\subset \mathbb{R}^n\), which is continuous in probability. The authors give sufficient conditions for the existence of a version of the random field \(\psi\) in a generalized Hölder space \(H_\rho ([0,1]^d)\) where \(\rho(\cdot)\) is the modulus of smoothness satisfying some conditions. A typical example of \(\rho(\cdot)\) is \(\rho(h)= h^\alpha \ln^\beta (c/h)\) where \(c\) is a suitable constant. They also discuss sufficient conditions for a central limit theorem to hold for i.i.d. or martingale difference sequences of random elements in \(H_\rho\).NEWLINENEWLINEFor the entire collection see [Zbl 0968.00043].