Euler approximations with varying coefficients: The case of superlinearly growing diffusion coefficients

By Sotirios Sabanis. 2013

204 citations recorded by the source corpus.

A new class of explicit Euler-type schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift and diffusion coefficients, is proposed in this article. It is shown, under very mild conditions, that these explicit schemes converge in probability and in L p to the solution of the corresponding SDEs. Moreover, rate of convergence estimates are provided for strong and almost sure convergence. In particular, the strong order 1/2 is recovered in the case of uniform L p -convergence.

Subfields: Computational Mechanics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3e7168e81d854e0b4858afed916be1bb5749a548

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In Computational Mechanics

1. George Yin
2. Xiaoyue Li
3. Xuerong Mao
4. Sotirios Sabanis
5. Chaman Kumar
6. István Gyöngy
7. Arnulf Jentzen

In Finance

1. George Yin
2. Xiaoyue Li
3. Xuerong Mao
4. Sotirios Sabanis
5. David Siska
6. Chaman Kumar
7. István Gyöngy
8. Arnulf Jentzen

In Mathematical Physics

1. George Yin
2. Xiaoyue Li
3. Xuerong Mao
4. Sotirios Sabanis
5. David Siska
6. Chaman Kumar
7. István Gyöngy
8. Ke Wang

Citations in the corpus

• Explicit numerical approximations for stochastic differential equations in finite and infinite horizons: truncation methods, convergence in pth moment, and stability (2019, methodology): “Talay (2002) obtained convergence rates for approximation to the invariant measures using an EM implicit scheme for a stochastic Hamiltonian dissipative system with nonglobal Lipschitz coefficients and additive noise. Lamberton & Pagès (2002, 2003) studied recursive stochastic algorithms with decrea”
• 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”
• Convergence of tamed Euler schemes for a class of stochastic evolution equations (2014, background): “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, background): “One could refer to [9], [10], [12], [19], [22], [24] and [20] for order 0.”