On the Generalized and Multi-mixed Generalized Grey Brownian Motions
In this paper we present a general mathematical construction that allows us to define a parametric class of non-Gaussian processes, namely generalized grey Brownian motion (ggBm) and multi-mixed generalized grey Brownian motions (mmggBm). For this purpose, we write down explicitly all the finite dimensional probability density functions and we provide different new properties associated with the ggBm characterizations. Next, the so-called multi-mixed generalized grey Brownian motions (mmggBm) are constructed by mixing by superimposing or mixing (infinitely many) independent generalized grey Brownian motions. Their existence as processes is proved, and their path properties, viz. long-range dependence and Hölder continuity are studied. As applications, we derive an explicit solutions of the Generalized Grey Ornstein-Uhlenbeck and of a linear Wick-type stochastic differential equation driven respectively by generalized grey Brownian motion and Multi-mixed generalized grey Brownian motions. The solutions are characterized to be in a suitable distribution space.
In this paper we present a general mathematical construction that allows us to define a parametric class of non-Gaussian processes, namely generalized grey Brownian motion (ggBm) and multi-mixed…
The main aim of this paper is to construct and emphasize certain properties of a new polynomial sequences called fractional Pascal appell polynomials associated with the infinite dimensional…
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