Consistency and Numerical Stability of the Euler Approximation for the Solution of Delay SDE’s with Possibly Discontinuous Initial Data

This study follows on from [1]'s work on Precise Estimates and [2]'s work on Approximation Theorems. We have shown that the S.F.D.E. Euler approximation considered in [2] and [1] is numerically stable and weakly consistent. Note that the introduction, notations,

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Precise Estimates for the Solution of Stochastic Functional Differential Equations with Discontinuous Initial Data: A Mathematical Approach

We have established a uniform error bound for the Euler approximation to the solution process of the Stochastic Funtional Differential Equation (S.F.D.E.) (1.11) over the entire time span in this chapter. We discovered the upper bound for the difference between

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Uniform Convergence of Euler Approximation of the Solution of Stochastic Functional Differential Equations with Discontinuous Initial Data

Because model Delay SDEs are often non-linear and do not allow for explicit solutions, numerical approximation approaches for solutions of delay stochastic equations are clearly required. Early explorations in this area were conducted in [1] and [2]. Many physical phenomenon

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