We study the asymptotic behaviour of stochastic processes that are generated by sums of partial sums of i.i.d. random variables and their renewals. We conclude that these processes cannot converge weakly to any nondegenerate random element of the space D[0, 1]. On the other hand we show that their properly normalized integrals as Vervaat-type stochastic processes converge weakly to a squared Wi...

The Riemann zeta process is a stochastic process {Z(σ), σ > 1} with independent increments and marginal distributions whose characteristic functions are proportional to the Riemann zeta function along vertical lines < s = σ . We establish functional limit theorems for the zeta process and other related processes as arguments σ approach the pole at s = 1 of the zeta function (from above).

The present paper addresses an effective cyber defense model by applying information fusion based game theoretical approaches‎. ‎In the present paper, we are trying to improve previous models by applying stochastic optimal control and robust optimization techniques‎. ‎Jump processes are applied to model different and complex situations in cyber games‎. ‎Applying jump processes we propose some m...

In recent articles the author used his work in measure and integration to produce a new universal concept of stochastic processes. This concept leads, for the first time, for a stochastic process to a natural notion of essential subsets in the path space. But there remained some contrast to the traditional treatment, for example because for the Poisson process the set of càdlàg paths is not an ...