Solving stochastic differential equations (SDEs) numerically, the explicit Euler-Maruyama (EM) schemes are used most frequently  under  the global Lipschitz conditions for both drift and diffusion coefficients. In contrast, without imposing the global Lipschitz conditions, implicit schemes are often used  for SDEs but require additional computational effort; along another line, tamed EM  schemes and truncated EM (TEM) schemes  have been developed recently.  In this talk, we will review the development of the TEM schemes.  We will briefly recall the original TEM scheme defined by Mao in 2015.  We will then explain how it has been modified to cope with the need in different aspects. We will mainly explain how to define a TEM scheme for the th moment boundedness while to define different TEM schemes for other asymptotic properties of the numerical solutions such as the exponential stability in th moment and stability in distribution. A couple of examples are given for illustration.

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