Convergence rate of Euler scheme for time-inhomogeneous SDEs involving the local time of the unknown process

2020 ◽  
Vol 36 (3) ◽  
pp. 452-472
Author(s):  
Mohamed Bourza ◽  
Mohsine Benabdallah
Keyword(s):  
Convergence Rate ◽  
Local Time ◽  
Euler Scheme

scholarly journals On the weak convergence rate of an exponential Euler scheme for SDEs governed by coefficients with superlinear growth

Bernoulli ◽  
2021 ◽  
Vol 27 (1) ◽  
pp. 312-347
Author(s):  
Mireille Bossy ◽  
Jean-François Jabir ◽  
Kerlyns Martínez
Keyword(s):  
Weak Convergence ◽  
Convergence Rate ◽  
Euler Scheme ◽  
Superlinear Growth ◽  
Weak Convergence Rate

Convergence of Finite Fifference Method for Parabolic Problem

2003 ◽  
Vol 3 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Dejan Bojović
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Parabolic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

Abstract In this paper we consider the first initial boundary-value problem for the heat equation with variable coefficients in a domain (0; 1)x(0; 1)x(0; T]. We assume that the solution of the problem and the coefficients of the equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

On the approximation of $ \ exp (-x) $ on the half-axis by spline functions in three-point rational interpolants

2019 ◽  
pp. 32-37
Author(s):  
Abdul-Rashid Ramazanov ◽  
V.G. Magomedova
Keyword(s):  
Convergence Rate ◽  
Spline Functions ◽  
Rational Spline ◽  
Rational Interpolants ◽  
Half Axis

For the function $f(x)=\exp(-x)$, $x\in [0,+\infty)$ on grids of nodes $\Delta: 0=x_0<x_1<\dots $ with $x_n\to +\infty$ we construct rational spline-functions such that $R_k(x,f, \Delta)=R_i(x,f)A_{i,k}(x)\linebreak+R_{i-1}(x, f)B_{i,k}(x)$ for $x\in[x_{i-1}, x_i]$ $(i=1,2,\dots)$ and $k=1,2,\dots$ Here $A_{i,k}(x)=(x-x_{i-1})^k/((x-x_{i-1})^k+(x_i-x)^k)$, $B_{i,k}(x)=1-A_{i,k}(x)$, $R_j(x,f)=\alpha_j+\beta_j(x-x_j)+\gamma_j/(x+1)$ $(j=1,2,\dots)$, $R_j(x_m,f)=f(x_m)$ при $m=j-1,j,j+1$; we take $R_0(x,f)\equiv R_1(x,f)$. Bounds for the convergence rate of $R_k(x,f, \Delta)$ with $f(x)=\exp(-x)$, $x\in [0,+\infty)$, are found.

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