Open AccessThe truncated Euler-Maruyama method for highly nonlinear neutral stochastic differential equations with time-dependent delay
Author(s) -
Aleksandra Petrovic,
Marija Milošević
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2107457p
Subject(s) - mathematics , lipschitz continuity , convergence (economics) , nonlinear system , stochastic differential equation , delay differential equation , euler's formula , euler method , backward euler method , completeness (order theory) , mathematical analysis , differential equation , euler equations , physics , quantum mechanics , economics , economic growth
The main goal of this paper is to establish the Lq-convergence of the truncated Euler-Maruyama method for neutral stochastic differential equations with time-dependent delay under the Khasminskii-type condition. Whole consideration is influenced by the presence of the neutral term and delay function. The main theoretical result is illustrated by an example. Since the main result is related to the Lq-convergence of the Euler-Maruyama method under the global Lipschitz condition on the coefficients of the equation under consideration, for completeness of the paper, the appropriate results are given in Appendix.