This paper describes the methodology used by team RedSea in data competition organized for EVA 2021 conference. We develop a novel two-part model to jointly describe wildfire count and burnt area provided organizers with covariates. Our proposed relies on integrated nested Laplace approximation combined stochastic partial differential equation (INLA-SPDE) approach. In first part, binary non-sta...

<p style='text-indent:20px;'>We consider the control of semilinear stochastic partial differential equations (SPDEs) via deterministic controls. In case multiplicative noise, existence optimal controls and necessary conditions for optimality are derived. additive we obtain a representation gradient cost functional adjoint calculus. The restriction to noise avoids necessity introducing bac...

In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.). So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreo...

Stochastic partial differential equations (SPDEs) are crucial for modelling dynamics with randomness in many areas including economics, physics, and atmospheric sciences. Recently, using deep learning approaches to learn the PDE solution accelerating simulation becomes increasingly popular. However, SPDEs have two unique properties that require new design on models. First, model approximate of ...

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift in Hilbert spaces are considered‎. ‎The coefficients are assumed to have linear growth‎. ‎We do not impose coercivity conditions on coefficients‎. ‎A novel method of proof for establishing existence and uniqueness of the mild solution is proposed‎. ‎Examples on stochastic partial differentia...

In this paper we introduce a new kind of Backward Stochastic Differential Equations, called ergodic BSDEs, which arise naturally in the study of optimal ergodic control. We study the existence, uniqueness and regularity of solution to ergodic BSDEs. Then we apply these results to the optimal ergodic control of a Banach valued stochastic state equation. We also establish the link between the erg...

Mathematical modeling and computer simulations are nowadays widely used tools to predict the behavior of problems in engineering and in the natural and social sciences. All such predictions are obtained by formulating mathematical models and then using computational methods to solve the corresponding problems. We use a probability theory approach for uncertainty quantification (UQ) since it is ...

We explore Itô stochastic differential equations where the drift term has possibly infinite dependence on the past. Assuming the existence of a Lyapunov function, we prove the existence of a stationary solution assuming only minimal continuity of the coefficients. Uniqueness of the stationary solution is proved if the dependence on the past decays sufficiently fast. The results of this paper ar...

We prove a general theorem that the L2ρ(R ;R) ⊗ L2ρ(R ;R) valued solution of an infinite horizon backward doubly stochastic differential equation, if exists, gives the stationary solution of the corresponding stochastic partial differential equation. We prove the existence and uniqueness of the L2ρ(R ;R)⊗Lρ(R ;R) valued solutions for backward doubly stochastic differential equations on finite a...