Consider a multidimensional SDE of the form Xt = x + ∫ t 0 b(Xs−)ds + ∫ t 0 f(Xs−)dZs where (Zs)s≥0 is a symmetric stable process. Under suitable assumptions on the coefficients the unique strong solution of the above equation admits a density w.r.t. the Lebesgue measure and so does its Euler scheme. Using a parametrix approach, we derive an error expansion w.r.t. the time step for the differen...

In the present work an attempt has been made to study the dynamics of a diatomic molecule N2 water. The proposed model consists of Langevin stochastic differential equation whose solution is obtained through Euler’s method. The proposed work has been concluded by studying the behavior of statistical parameters like variance in position, variance in velocity and covariance between position and v...

Let V be a closed subscheme of a projective space P. We give an algorithm to compute the Chern-Schwartz-MacPherson class, and the Euler characteristic of V and an algorithm to compute the Segre class of V . The algorithms can be implemented using either symbolic or numerical methods. The algorithms are based on a new method for calculating the projective degrees of a rational map defined by a h...

A theory of systems of differential equations of the form dy = ∑ j f i j(y)dx , where the driving path x(t) is non-differentiable, has recently been developed by Lyons. We develop an alternative approach to this theory, using (modified) Euler approximations, and investigate its applicability to stochastic differential equations driven by Brownian motion. We also give some other examples showing...

In this work, we approximate a diffusion process by its Euler scheme and we study the convergence of the density of the marginal laws. We improve previous estimates especially for small time.

We generalise the current theory of optimal strong convergence rates for implicit Euler-based methods by allowing for Poisson-driven jumps in a stochastic differential equation (SDE). More precisely, we show that under one-sided Lipschitz and polynomial growth conditions on the drift coefficient and global Lipschitz conditions on the diffusion and jump coefficients, three variants of backward E...

Abstract: This paper gives some sufficient conditions for a given polyhedral set which is represented as a set of linear inequalities to be positive D-invariant for uncertain linear discrete-time systems in the case such that the systems matrices depend linearly on uncertain parameters whose ranges are given intervals. Further, the results will be applied to uncertain linear continuous systems ...

In this paper, the improved Euler method is used for solving hybrid fuzzy fractional differential equations (HFFDE) of order q ∈ (0,1) under Caputo-type fuzzy fractional derivatives. This method is based on the fractional Euler method and generalized Taylor’s formula. The accuracy and efficiency of the proposed method is demonstrated by solving numerical examples.

We prove strong convergence of order [Formula: see text] for arbitrarily small [Formula: see text] of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient. The proof is based on estimating the difference between the Euler-Maruyama scheme and another numerical method, which is constructed by applying...

This paper presents an efficient Euler method on Cartesian grids coupled with an integral Boundary-Layer method. The unsteady Euler equations are solved using cell-centered finite volume method by the implicit-explicit dual-time stepping scheme. The wall boundary conditions on the wing are implemented on the wing chord plane by first order approximation so that non-moving Cartesian grids can be...