scholarly journals Strong Convergence Rates of Wavelet Estimators in Semiparametric Regression Models with Censored Data*

2008 ◽  
Vol 2 (1) ◽  
pp. 8-13 ◽  
Author(s):  
Hongchang Hu
Keyword(s):  
Strong Convergence ◽  
Censored Data ◽  
Regression Models ◽  
Convergence Rates ◽  
Semiparametric Regression ◽  
Wavelet Estimators ◽  
Strong Convergence Rates

scholarly journals First-order convergence of Milstein schemes for McKean–Vlasov equations and interacting particle systems

2021 ◽  
Vol 477 (2245) ◽  
pp. 20200258
Author(s):  
Jianhai Bao ◽  
Christoph Reisinger ◽  
Panpan Ren ◽  
Wolfgang Stockinger
Keyword(s):  
Strong Convergence ◽  
Convergence Rates ◽  
Interacting Particle Systems ◽  
Particle System ◽  
First Order ◽  
Time Stepping ◽  
Vlasov Equations ◽  
Interacting Particle ◽  
Moment Stability ◽  
Strong Convergence Rates

In this paper, we derive fully implementable first-order time-stepping schemes for McKean–Vlasov stochastic differential equations, allowing for a drift term with super-linear growth in the state component. We propose Milstein schemes for a time-discretized interacting particle system associated with the McKean–Vlasov equation and prove strong convergence of order 1 and moment stability, taming the drift if only a one-sided Lipschitz condition holds. To derive our main results on strong convergence rates, we make use of calculus on the space of probability measures with finite second-order moments. In addition, numerical examples are presented which support our theoretical findings.

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