A Strongly Monotonic Polygonal Euler Scheme

12/31/2021

∙

Rate of convergence results are presented for a new class of explicit Euler schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift coefficients that satisfy a particular form of strong monotonicity. The new, distinct feature of this class of explicit schemes is the preservation of the monotonicity condition for the new, suitably controlled drift coefficients that guaranty the finiteness of moments of the numerical solutions up to a desired order.

READ FULL TEXT

A Strongly Monotonic Polygonal Euler Scheme

Well-posedness and tamed Euler schemes for McKean-Vlasov equations driven by Lévy noise

Polynomial propagation of moments in stochastic differential equations

Convergence of the tamed-Euler-Maruyama method for SDEs with discontinuous and polynomially growing drift

Uniform minorization condition and convergence bounds for discretizations of kinetic Langevin dynamics

Hybrid, adaptive, and positivity preserving numerical methods for the Cox-Ingersoll-Ross model

Compositions of pseudo-symmetric integrators with complex coefficients for the numerical integration of differential equations

Strong convergence of the tamed Euler scheme for scalar SDEs with superlinearly growing and discontinuous drift coefficient

A Strongly Monotonic Polygonal Euler Scheme

Related Research

Well-posedness and tamed Euler schemes for McKean-Vlasov equations driven by Lévy noise

Polynomial propagation of moments in stochastic differential equations

Convergence of the tamed-Euler-Maruyama method for SDEs with discontinuous and polynomially growing drift

Uniform minorization condition and convergence bounds for discretizations of kinetic Langevin dynamics

Hybrid, adaptive, and positivity preserving numerical methods for the Cox-Ingersoll-Ross model

Compositions of pseudo-symmetric integrators with complex coefficients for the numerical integration of differential equations

Strong convergence of the tamed Euler scheme for scalar SDEs with superlinearly growing and discontinuous drift coefficient