A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

The emergence of corona virus (COVID-19) has create a great public concern as the outbreak is still ongoing and government are taking actions such as holiday extension, travel restriction, temporary closure of public work place, borders, schools, quarantine/isolation, social distancing and so on. To mitigate the spread, we proposed and analyzed a stochastic model for the continue spread of coro...

A necessary and suucient condition is given to reduce a non-stationary random process fZ(t) : t 2 T Rg to stationarity via a bijective diieren-tiable time deformation so that its correlation function r(t; t 0) depends only on the diierence (t 0)?(t) through a stationary correlation function R: r(t; t 0) = R(((t 0) ? (t)).

Logarithmic asymptotics are proved for the tail of the supremum of a stochastic process, under the assumption that the process satisfies a restricted large deviation principle on regularly varying scales. The formula for the rate of decay of the tail of the supremum, in terms of the underlying rate function, agrees with that stated by Duffield and O’Connell [Math. Proc. Cambridge Philos. Soc. (...

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).

In this paper, we examine the research and results of dynamic pricing policies and their relation to revenue management. The survey is based on a generic revenue management problem in which a perishable and nonrenewable set of resources satisfy stochastic pricesensitive demand processes over a finite period of time. In this class of problems, the owner (or the seller) of these resources uses th...

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 ...