Geodesic
The truncated Euler–Maruyama method for highly nonlinear neutral stochastic differential equations with time-dependent delay
Filomat, Tome 35 (2021) no. 7, p. 2457

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DOI

The main goal of this paper is to establish the L q-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 L q-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
DOI : 10.2298/FIL2107457P
Classification : 60H10 60H35
Keywords: Neutral stochastic differential equations, time-dependent delay, Khasminskii-type condition, truncated Euler– Maruyama approximation, Lq-convergence 
Aleksandra Petrović; Marija Milošević. The truncated Euler–Maruyama method for highly nonlinear neutral stochastic differential equations with time-dependent delay. Filomat, Tome 35 (2021) no. 7, p. 2457 . doi: 10.2298/FIL2107457P
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     author = {Aleksandra Petrovi\'c and Marija Milo\v{s}evi\'c},
     title = {The truncated {Euler{\textendash}Maruyama} method for highly nonlinear neutral stochastic differential equations with time-dependent delay},
     journal = {Filomat},
     pages = {2457 },
     year = {2021},
     volume = {35},
     number = {7},
     doi = {10.2298/FIL2107457P},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2107457P/}
}
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