Carathéodory’s approximate solution to stochastic differential delay equation. (English) Zbl 1412.60077
Summary: In this paper, we show the difference between an approximate solution and an accurate solution for a stochastic differential delay equation, where the approximate solution, which is called by Carathéodory, is constructed by successive approximation. Furthermore, we study the \(p\)-th moment continuity of the approximate solution for this delay equation.
MSC:
| 60H05 | Stochastic integrals |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H20 | Stochastic integral equations |
Keywords:
Hölder inequality; moment inequality; Carathéodory approximation procedure; stochastic differential delay equationReferences:
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