Numerical Integration of Stochastic Differential Equations

By Rüdiger U. Seydel. 2004

138 citations recorded by the source corpus.

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Citations in the corpus

Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients (2014, background): “, the monographs Kloeden & Platen [20] and Milstein [26].”
Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients (2009, unknown): “It is a classical result (see, e.g., Kloeden & Platen 1992 and Milstein 1995) that the Euler approximation converges in case of globally Lipschitz continuous drift and diﬀusion coeﬃcient functions.”
Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms (2015, background): “The basic idea of the proof is similar to the classical approach in proving weak convergence of discretization schemes of SDEs outlined in the seminal papers by Milstein (Milstein (1975, 1979, 1986, 1995)).”
Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients (2010, unknown): “In the literature (see, e.g., Theorem 10. in Kloeden and Platen [20], Theorem 1.1 in Milstein [27] or Theorem 3.1 in Yuan and Mao [38]) the convergence results for the explicit Euler scheme require the drift coeﬃcient µ of the SDE (1) to be globally Lipschitz continuous or to grow at most linearly,…”
Scalable Gradients for Stochastic Differential Equations (2020, background): “Milstein [50] and stochastic Runge-Kutta [68]) without approximating multiple integrals or the Lévy area during simulation.”
Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion (2006, methodology): “For the approximation of Itˆo-SDEs with respect to mean square error criterions, see, e.g., [12] or [16] and Remark 2, point 3.”
An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process (2012, background): “Thus, the standard theory that relies on the global Lipschitz assumption does not apply (Milstein 1995; Kloeden & Platen 1999).”
Loss of regularity for Kolmogorov equations (2012, background): “, the books and overview articles [42, 43, 52, 24, 3, 53, 56, 38, 41] for extensive lists of references.”
Comparative Analysis of the Efficiency of Application of Legendre Polynomials and Trigonometric Functions to the Numerical Integration of Ito Stochastic Differential Equations (2018, unknown): “Let us consider an another approach to the expansion of iterated Ito stochastic integrals [4]-[43] (method of generalized multiple Fourier series).”