We study stochastic partial differential equations (SPDEs) with potentially very rough fractional noise Hurst parameter [Formula: see text]. Close to a change of stability measured small text], we rely on the natural separation time-scales and establish simplified description essential dynamics. Up an error term bounded by power text] depending can approximate solution SPDE in first order SDE, ...

• A linear quadratic problem of BSDE under partial information is solved completely. different decoupling technique used to solve stochastic Hamiltonian system. feedback representation optimal control obtained. An explicit formula cost established. solvability with filtering first studied. In this paper, we study an backward differential equation (BSDE) functional information. This completely a...

Preventive maintenance is widely used in wind turbine equipment to ensure their safe and reliable operation, this mainly includes time-based (TBM) condition-based (CBM). Most farms only use TBM as the main strategy engineering practice. Although can meet certain reliability requirements, it cannot fully utilize characteristics of CBM. For this, a state model based on stochastic differential equ...

chloride ion ingress in concrete is the main reason of concrete corrosion. in real world both uncertainty and stochasticity are main attributes of almost all measurements including testing and modeling of chloride content profile in concrete. regarding these facts new models should be able to represent at least some of the uncertainties in the predictions. in this paper after inspiration from c...

Continuous approximations that are ordinary differential equations (ODEs) or stochastic differential equations (SDEs) are often used to study the properties of discrete stochastic processes. We show that different ways of taking the continuous limit of the same model may result in either an ODE or a SDE and study the manner in which each approximates the discrete model. We compare the asymptoti...

We provide existence and uniqueness of global (and local) mild solutions for a general class of semilinear stochastic partial differential equations driven by Wiener processes and Poisson random measures under local Lipschitz and linear growth (or local boundedness, resp.) conditions. The socalled “method of the moving frame” allows us to reduce the SPDE problems to SDE problems.

We propose two Euler–Maruyama (EM) type numerical schemes in order to approximate the invariant measure of a stochastic differential equation (SDE) driven by an α-stable Lévy process (1<α<2): approximation scheme with distributed noise and further Pareto-distributed noise. Using discrete version Duhamel’s principle Bismut’s formula Malliavin calculus, we prove that error bounds Wasserstein-1 di...

Milstein and approximate coupling approaches are compared for the pathwise numerical solutions to stochastic differential equations (SDE) driven by Brownian motion. These methods attain an order one convergence under nondegeneracy assumption of diffusion term method. We use MATLAB simulate these applying them a particular two-dimensional SDE. Then, we analyze performance both amount time requir...

Maize yield prediction in the sub-Saharan region is imperative for mitigation of risks emanating from crop loss due to changes climate. Temperature, rainfall amount, and reference evapotranspiration are major climatic factors affecting maize yield. They not only interdependent but also have significantly changed climate change, which causes nonlinearity nonstationarity weather data. Hence, ther...

Relatively little is known about the ability of numerical methods for stochastic differential equations (SDEs) to reproduce almost sure and small-moment stability. Here, we focus on these stability properties in the limit as the timestep tends to zero. Our analysis is motivated by an example of an exponentially almost surely stable nonlinear SDE for which the Euler–Maruyama (EM) method fails to...