Well-posedness and tamed schemes for McKean–Vlasov equations with common noise
In this paper, we first establish well-posedness of McKean–Vlasov stochastic differential
equations (McKean–Vlasov SDEs) with common noise, possibly with coefficients of super …
equations (McKean–Vlasov SDEs) with common noise, possibly with coefficients of super …
[HTML][HTML] The truncated EM method for stochastic differential equations with Poisson jumps
In this paper, we use the truncated Euler–Maruyama (EM) method to study the finite time
strong convergence for SDEs with Poisson jumps under the Khasminskii-type condition. We …
strong convergence for SDEs with Poisson jumps under the Khasminskii-type condition. We …
On explicit Milstein-type scheme for McKean–Vlasov stochastic differential equations with super-linear drift coefficient
We introduce an explicit Milstein-type scheme for McKean–Vlasov stochastic differential
equations using the notion of a measure derivative given by P.-L. Lions in his lectures at the …
equations using the notion of a measure derivative given by P.-L. Lions in his lectures at the …
Strong and weak divergence of exponential and linear-implicit Euler approximations for stochastic partial differential equations with superlinearly growing …
M Beccari, M Hutzenthaler, A Jentzen… - arXiv preprint arXiv …, 2019 - arxiv.org
The explicit Euler scheme and similar explicit approximation schemes (such as the Milstein
scheme) are known to diverge strongly and numerically weakly in the case of one …
scheme) are known to diverge strongly and numerically weakly in the case of one …
On the infinite time horizon approximation for Lévy-driven McKean-Vlasov SDEs with non-globally Lipschitz continuous and super-linearly growth drift and diffusion …
This paper studies the numerical approximation for McKean-Vlasov stochastic differential
equations driven by Lévy processes. We propose a tamed-adaptive Euler-Maruyama …
equations driven by Lévy processes. We propose a tamed-adaptive Euler-Maruyama …
[HTML][HTML] Convergence and stability of the backward Euler method for jump–diffusion SDEs with super-linearly growing diffusion and jump coefficients
Z Chen, S Gan - Journal of Computational and Applied Mathematics, 2020 - Elsevier
This paper firstly investigates convergence of the backward Euler method for stochastic
differential equations (SDEs) driven by Brownian motion and compound Poisson process …
differential equations (SDEs) driven by Brownian motion and compound Poisson process …
[HTML][HTML] On explicit tamed Milstein-type scheme for stochastic differential equation with Markovian switching
We propose a new tamed Milstein-type scheme for stochastic differential equation with
Markovian switching when drift coefficient is assumed to grow super-linearly. The strong rate …
Markovian switching when drift coefficient is assumed to grow super-linearly. The strong rate …
Mean-square approximations of L\'{e} vy noise driven SDEs with super-linearly growing diffusion and jump coefficients
Z Chen, S Gan, X Wang - arXiv preprint arXiv:1812.03069, 2018 - arxiv.org
This paper first establishes a fundamental mean-square convergence theorem for general
one-step numerical approximations of L\'{e} vy noise driven stochastic differential equations …
one-step numerical approximations of L\'{e} vy noise driven stochastic differential equations …
Taming the Interactive Particle Langevin Algorithm--the superlinear case
T Johnston, N Makras, S Sabanis - arXiv preprint arXiv:2403.19587, 2024 - arxiv.org
Recent advances in stochastic optimization have yielded the interactive particle Langevin
algorithm (IPLA), which leverages the notion of interacting particle systems (IPS) to efficiently …
algorithm (IPLA), which leverages the notion of interacting particle systems (IPS) to efficiently …
Well-posedness and tamed Euler schemes for McKean-Vlasov equations driven by L\'evy noise
We prove the well-posedness of solutions to McKean-Vlasov stochastic differential
equations driven by L\'evy noise under mild assumptions where, in particular, the L\'evy …
equations driven by L\'evy noise under mild assumptions where, in particular, the L\'evy …