
Approximation of the invariant distribution for a class of ergodic SPDEs using an explicit tamed exponential Euler scheme
We consider the longtime behavior of an explicit tamed exponential Eule...
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Strong convergence of an adaptive timestepping Milstein method for SDEs with onesided Lipschitz drift
We introduce explicit adaptive Milstein methods for stochastic different...
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Error Bounds of the Invariant Statistics in Machine Learning of Ergodic Itô Diffusions
This paper studies the theoretical underpinnings of machine learning of ...
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Approximation of solutions of DDEs under nonstandard assumptions via Euler scheme
We deal with approximation of solutions of delay differential equations ...
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Taming singular stochastic differential equations: A numerical method
We consider a generic and explicit tamed Euler–Maruyama scheme for multi...
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Control Synthesis of Nonlinear Sampled Switched Systems using Euler's Method
In this paper, we propose a symbolic control synthesis method for nonlin...
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An Analysis of the Milstein Scheme for SPDEs without a Commutative Noise Condition
In order to approximate solutions of stochastic partial differential equ...
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Approximation of the invariant distribution for a class of ergodic SDEs with onesided Lipschitz continuous drift coefficient using an explicit tamed Euler scheme
We consider the longtime behavior of an explicit tamed Euler scheme applied to a class of stochastic differential equations driven by additive noise, under a onesided Lipschitz continuity condition. The setting encompasses drift nonlinearities with polynomial growth. First, we prove that moment bounds for the numerical scheme hold, with at most polynomial dependence with respect to the time horizon. Second, we apply this result to obtain error estimates, in the weak sense, in terms of the timestep size and of the time horizon, to quantify the error to approximate averages with respect to the invariant distribution of the continuoustime process. We justify the efficiency of using the explicit tamed Euler scheme to approximate the invariant distribution, since the computational cost does not suffer from the at most polynomial growth of the moment bounds. To the best of our knowledge, this is the first result in the literature concerning the approximation of the invariant distribution for SDEs with nonglobally Lipschitz coefficients using an explicit tamed scheme.
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