A note on tamed Euler approximations

By Sotirios Sabanis. 2013

230 citations recorded by the source corpus.

Strong convergence results on tamed Euler schemes, which approximate stochastic differential equations with superlinearly growing drift coefficients that are locally one-sided Lipschitz continuous, are presented in this article. The diffusion coefficients are assumed to be locally Lipschitz continuous and have at most linear growth. Furthermore, the classical rate of convergence, i.e. one-half, for such schemes is recovered when the local Lipschitz continuity assumptions are replaced by global and, in addition, it is assumed that the drift coefficients satisfy polynomial Lipschitz continuity.

Subfields: Demography, Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/47c5017a2b1fc27886c5b83ab787152f5ebe6845

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Demography

In Economics and Econometrics

In Finance

Citations in the corpus

Simulation of McKean–Vlasov SDEs with super-linear growth (2018, methodology): “Since then several authors have built on this result and developed algorithms to deal with coefficients that grow super-linearly, see [8], [27], [13] for example.”
Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities (2015, unknown): “, [2], [11], [12], [20], [26], [27], [28], [29], [31], [32], and the references mentioned in”
Euler approximations with varying coefficients: The case of superlinearly growing diffusion coefficients (2013, methodology): “1 Introduction Motivated by the work of [11] and [6] on explicit Euler-type schemes which approximate (in an Lp sense) SDEs with superlinearly growing drift coefficients, the author extends the techniques developed in [11] and [3] to obtain, under very mild assumptions, convergence results for the c”
Convergence of tamed Euler schemes for a class of stochastic evolution equations (2014, methodology): “Further work on explicit numerical approximations of stochastic differential equations with super-linearly growing coefficients can be found in Tretyakov and Zhang [19], Hutzenthaler and Jentzen [12], Sabanis [17] aswellDareiotis, Kumar andSabanis [18].”
On tamed milstein schemes of SDEs driven by Lévy noise (2014, methodology): “Further, our calculations are motivated by the classical methodology (see also [3, 15]) and hence are more refined than those present in the literature.”
The truncated Euler-Maruyama method for stochastic differential equations (2015, methodology): “This method was further developed in [32] while the tamed Milstein method was developed in [6].”
Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in pth moment, and stability (2019, background): “We approximate the exact solution by piecewise constant interpolation directly, which is different from that of the studies by Higham et al. (2002), Hutzenthaler et al. (2012), Sabanis (2013), Mao (2015) and Bao et al. (2016).”