• Corpus ID: 247958046

Existence, uniqueness and approximation of solutions of SDEs with superlinear coefficients in the presence of discontinuities of the drift coefficient

@inproceedings{MullerGronbach2022ExistenceUA,
  title={Existence, uniqueness and approximation of solutions of SDEs with superlinear coefficients in the presence of discontinuities of the drift coefficient},
  author={Thomas Muller-Gronbach and Sotirios Sabanis and Larisa Yaroslavtseva},
  year={2022}
}
. Existence, uniqueness, and L p -approximation results are presented for scalar stochastic differential equations (SDEs) by considering the case where, the drift coefficient has finitely many spatial discontinuities while both coefficients can grow superlinearly (in the space variable). These discontinuities are described by a piecewise local Lipschitz continuity and a piecewise monotone-type condition while the diffusion coefficient is assumed to be locally Lipschitz continuous and non-degenerate at… 

Convergence of the tamed-Euler-Maruyama method for SDEs with discontinuous and polynomially growing drift

Numerical methods for SDEs with irregular coefficients are intensively studied in the literature, with different types of irregularities usually being attacked separately. In this paper we combine two

A higher order approximation method for jump-diffusion SDEs with discontinuous drift coefficient

We present the first higher-order approximation scheme for solutions of jump-diffusion stochastic differential equations with discontinuous drift. For this transformation-based jump-adapted

Strong convergence of the tamed Euler scheme for scalar SDEs with superlinearly growing and discontinuous drift coefficient

In this paper, we consider scalar stochastic differential equations (SDEs) with a superlinearly growing and piecewise continuous drift coefficient. Existence and uniqueness of strong solutions of

References

SHOWING 1-10 OF 45 REFERENCES

A numerical method for SDEs with discontinuous drift

A transformation technique is introduced, which can on the one hand be used to prove existence and uniqueness for a class of SDEs with discontinuous drift coefficient and on the other hand a numerical method based on transforming the Euler–Maruyama scheme is presented.

On the performance of the Euler–Maruyama scheme for SDEs with discontinuous drift coefficient

Recently a lot of effort has been invested to analyze the $L_p$-error of the Euler-Maruyama scheme in the case of stochastic differential equations (SDEs) with a drift coefficient that may have

Convergence of the tamed-Euler-Maruyama method for SDEs with discontinuous and polynomially growing drift

Numerical methods for SDEs with irregular coefficients are intensively studied in the literature, with different types of irregularities usually being attacked separately. In this paper we combine two

Polygonal Unadjusted Langevin Algorithms: Creating stable and efficient adaptive algorithms for neural networks

A new class of Langevin based algorithms, which overcomes many of the known shortcomings of popular adaptive optimizers that are currently used for the fine tuning of deep learning models, and is named THεO POULA (or, simply, TheoPouLa).

An adaptive strong order 1 method for SDEs with discontinuous drift coefficient

  • L. Yaroslavtseva
  • Mathematics
    Journal of Mathematical Analysis and Applications
  • 2022

Quantifying a convergence theorem of Gy\"ongy and Krylov

We derive sharp strong convergence rates for the Euler–Maruyama scheme approximating multidimensional SDEs with multiplicative noise without im-posing any regularity condition on the drift

Sharp lower error bounds for strong approximation of SDEs with discontinuous drift coefficient by coupling of noise

In the past decade, an intensive study of strong approximation of stochastic differential equations (SDEs) with a drift coefficient that has discontinuities in space has begun. In the majority of

Taming neural networks with TUSLA: Non-convex learning via adaptive stochastic gradient Langevin algorithms

This work offers a new learning algorithm based on an appropriately constructed variant of the popular stochastic gradient Langevin dynamics (SGLD), which is called tamed unadjusted Stochastic Langevin algorithm (TUSLA), and provides finite-time guarantees for TUSLA to find approximate minimizers of both empirical and population risks.

Adaptive Euler–Maruyama method for SDEs with nonglobally Lipschitz drift

This paper, based on two main papers Fang and Giles (Adaptive Euler–Maruyama method for SDEs with non-globally Lipschitz drift: Part I, finite time interval, 2016, [2]), Fang and Giles (Adaptive

A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT

In this paper we construct a one-to-one (and quasi-isometric) transformation of a phase space that allows us to pass from a diffusion process with nonzero drift coefficient to a process without