scholarly journals Strong convergence rates for markovian representations of fractional processes

2017 ◽  
Vol 22 (11) ◽  
pp. 0-0
Author(s):  
Philipp Harms ◽  
Keyword(s):  
Strong Convergence ◽  
Convergence Rates ◽  
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.

scholarly journals Strong convergence rates for an explicit numerical approximation method for stochastic evolution equations with non-globally Lipschitz continuous nonlinearities

2019 ◽  
Vol 40 (2) ◽  
pp. 1005-1050 ◽  
Author(s):  
Arnulf Jentzen ◽  
Primož Pušnik
Keyword(s):  
Strong Convergence ◽  
Approximation Method ◽  
Evolution Equations ◽  
Convergence Rates ◽  
Reaction Diffusion ◽  
Convergence Result ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Lipschitz Continuous ◽  
Strong Convergence Rates

Abstract In this article we propose a new, explicit and easily implementable numerical method for approximating a class of semilinear stochastic evolution equations with non-globally Lipschitz continuous nonlinearities. We establish strong convergence rates for this approximation method in the case of semilinear stochastic evolution equations with globally monotone coefficients. Our strong convergence result, in particular, applies to a class of stochastic reaction–diffusion partial differential equations.

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