Based on the notion of paracontrolled distributions, we provide existence and uniqueness results for rough Volterra equations convolution type with potentially singular kernels driven by newly introduced class convolutional paths. The such paths above a wide stochastic processes including fractional Brownian motion is shown. As applications consider various types (partial) differential as delay...

We propose a coarse-graining procedure for describing the superhorizon dynamics of inflationary tensor modes. Our aim is to formulate stochastic description statistics spin-2 modes which seed background gravitational waves from inflation. Using basic principles quantum mechanics, we determine probability density coarse-grained fields, satisfies Fokker-Planck equation at scales. The correspondin...

Ships play the major role in bulk transportation and they need their special energy system. This paper proposes a stochastic programing method for optimal sizing of a hybrid ship power system with energy storage system (ESS), photovoltaic power (PV) and diesel generator. To account for uncertainties, in this study a two-stage stochastic mixed-integer non-linear programing is used to model the o...