Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Stability and convergence of the Euler scheme for stochastic linear evolution equations in Banach spaces

Binjie Li, Xiaoping Xie

Abstract

For the Euler scheme of the stochastic linear evolution equations, discrete stochastic maximal $ L^p $-regularity estimate is established, and a sharp error estimate in the norm $ \|\cdot\|_{L^p((0,T)\timesΩ;L^q(\mathcal O))} $, $ p,q \in [2,\infty) $, is derived via a duality argument.

Stability and convergence of the Euler scheme for stochastic linear evolution equations in Banach spaces

Abstract

For the Euler scheme of the stochastic linear evolution equations, discrete stochastic maximal -regularity estimate is established, and a sharp error estimate in the norm , , is derived via a duality argument.
Paper Structure (7 sections, 13 theorems, 143 equations, 1 figure)

This paper contains 7 sections, 13 theorems, 143 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Stability estimates
  4. Proof of
  5. Proof of
  6. Convergence estimate
  7. Some technical estimates

Key Result

Lemma 2.1

For any $p,q \in (1,\infty)$, there exist two positive constants $c_0$ and $c_1$ such that for all $f \in L_\mathbb F^p(\Omega;L^q(\mathcal{O};L^2(\mathbb R_{+};H)))$.

Figures (1)

  • Figure 1: The orientations of $\Upsilon_1$, $\Upsilon_2$ and $\partial\Sigma_{\theta_A}$.

Theorems & Definitions (24)

  • Lemma 2.1
  • Theorem 3.1
  • Theorem 3.2
  • Remark 3.1
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • Lemma 3.3
  • Lemma 3.4
  • proof
  • ...and 14 more