in this paper, we propose a new method for solving the stochastic advection-diffusion equation of ito type. in this work, we use a compact finite difference approximation for discretizing spatial derivatives of the mentioned equation and semi-implicit milstein scheme for the resulting linear stochastic system of differential equation. the main purpose of this paper is the stability investigatio...

In this paper, we first study the existence-uniqueness and large deviation estimate of solutions for stochastic Volterra integral equations with singular kernels in 2-smooth Banach spaces. Then, we apply them to a large class of semilinear stochastic partial differential equations (SPDE) driven by Brownian motions as well as by fractional Brownian motions, and obtain the existence of unique max...

Abstract. In this article, using DiPerna-Lions theory [1], we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, we also prove the L1integrability and a general maximal principle for generalized solutions of SPDEs. As applications, we study nonlinea...

For Kolmogorov equations associated to finite dimensional stochastic differential (SDEs) in high dimension, a numerical method alternative Monte Carlo simulations is proposed. The structure of the SDE inspired by Partial Differential Equations (SPDE) and thus contains an underlying Gaussian process which key algorithm. A series development solution terms iterated integrals given, it proved conv...

Abstract. Motivated by the concept of “location uncertainty”, initially introduced in Mémin (2014), a scheme is sought to perturb “location” state variable at every forecast time step. Further considering Brenier's theorem (Brenier, 1991), asserting that difference two positive density fields on same domain can be represented transportation map, we demonstrate perturbations consistently define ...

Abstract Bistability is a key property of many systems arising in the nonlinear sciences. For example, it appears partial differential equations (PDEs). scalar bistable reaction-diffusions PDEs, case even has taken on different names within communities such as Allee, Allen-Cahn, Chafee-Infante, Nagumo, Ginzburg-Landau, $$\Phi ^4$$ <mml:m...

We extend Peng's maximum principle for semilinear stochastic partial differential equations (SPDEs) in one space-dimension with non-convex control domains and control-dependent diffusion coefficients to the case of general cost functionals Nemytskii-type coefficients. Our analysis is based on a new approach characterization second order adjoint state as solution function-valued backward SPDE.

The principles behind the interface to continuous domain spatial models in the RINLA software package for R are described. The Integrated Nested Laplace Approximation (INLA) approach proposed by Rue, Martino, and Chopin (2009) is a computationally effective alternative to MCMC for Bayesian inference. INLA is designed for latent Gaussian models, a very wide and flexible class of models ranging f...

Uncertainty in the prediction of future weather is commonly assessed through the use of forecast ensembles that employ a numerical weather prediction model in distinct variants. Statistical postprocessing can correct for biases in the numerical model and improves calibration. We propose a Bayesian version of the standard ensemble model output statistics (EMOS) postprocessing method, in which sp...