Rectified deep neural networks overcome the curse of dimensionality when approximating solutions of McKean-Vlasov stochastic differential equations
DOI10.1016/j.jmaa.2024.128661zbMath1548.65042MaRDI QIDQ6614361
Tuan Anh Nguyen, Ariel Neufeld
Publication date: 7 October 2024
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
curse of dimensionalitycomplexity analysisMcKean-Vlasov SDEshigh-dimensional SDEsmultilevel Picard approximationrectified deep neural networks
Artificial neural networks and deep learning (68T07) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)
Cites Work
- Unnamed Item
- Ecole d'été de probabilités de Saint-Flour XIX, France, du 16 août au 2 septembre 1989
- Proof that deep artificial neural networks overcome the curse of dimensionality in the numerical approximation of Kolmogorov partial differential equations with constant diffusion and nonlinear drift coefficients
- Well-posedness and tamed schemes for McKean-Vlasov equations with common noise
- Well-posedness and numerical schemes for one-dimensional McKean-Vlasov equations and interacting particle systems with discontinuous drift
- Approximations of McKean-Vlasov stochastic differential equations with irregular coefficients
- A flexible split-step scheme for solving McKean-Vlasov stochastic differential equations
- A proof that rectified deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear heat equations
- An adaptive Euler-Maruyama scheme for Mckean-Vlasov SDEs with super-linear growth and application to the mean-field Fitzhugh-Nagumo model
- Deep ReLU network expression rates for option prices in high-dimensional, exponential Lévy models
- Antithetic multilevel sampling method for nonlinear functionals of measure
- Multilevel Picard approximations for McKean-Vlasov stochastic differential equations
- Iterative multilevel particle approximation for McKean-Vlasov SDEs
- Freidlin-Wentzell LDP in path space for McKean-Vlasov equations and the functional iterated logarithm law
- Numerical resolution of McKean-Vlasov FBSDEs using neural networks
- New particle representations for ergodic McKean-Vlasov SDEs
- Simulation of McKean–Vlasov SDEs with super-linear growth
- A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS
- Deep ReLU neural networks overcome the curse of dimensionality for partial integrodifferential equations
- A Proof that Artificial Neural Networks Overcome the Curse of Dimensionality in the Numerical Approximation of Black–Scholes Partial Differential Equations
- Importance sampling for McKean-Vlasov SDEs
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