Sample path properties of fractional Riesz–Bessel field of variable order

In this paper we consider fractional Riesz–Bessel field of variable order, which is also known as multifractional Riesz–Bessel field. Sample path properties of this random field such as local regularity, locally self-similar property, Hausdorff dimension of the graph, and long∕short range dependent property are studied. The relationship between the multifractional Riesz–Bessel field and the multifractional Brownian field is also established.