The continuity of Gaussian processes is an extensively studied topic and it culminates in Talagrand’s notion of majorizing measures that gives complicated necessary and sufficient conditions. In this note we study the Hölder continuity of Gaussian processes. It turns out that necessary and...

In this paper, we establish a version of the Feynman–Kac formula for multidimensional stochastic heat equation driven by a general semimartingale. This Feynman–Kac formula is then applied to study some nonlinear stochastic heat equations driven by nonhomogeneous Gaussian noise: first, an...

We consider parametric primal and dual Ky Fan inequalities in metric linear spaces. Sufficient conditions for Hölder continuity of solutions are established. Many examples are provided to illustrate the essentialness of the imposed assumptions and advantages of the results over existing ones....

The independent-oscillator model is thought to be a simple model for Brownian motion, explored extensively by Ford, Lewis and O'Connell. This model does not specify the distribution of the oscillators’ frequencies. By considering the distribution to be of two standard limits, otherwise...

In this paper, we have obtained recurrence relations for higher moments of order statistics from doubly truncated Burr distribution, which enable one to obtain all the single, double (product) and higher moments of any order of all order statistics for any sample size from doubly truncated Burr...

We present recurrence relations for the moments of order statistics from the Topp–Leone distribution without any restriction for the shape parameter. Several relations are also derived when the shape parameter is an integer. An application of the results is provided.