A Fundamental Mean-Square Convergence Theorem for SDEs with Locally Lipschitz Coefficients and Its Applications

2013/01/01 by M. V. Tretyakov, Z. Zhang · 5 citations
Economics, Econometrics and Finance · Physics and Astronomy · Decision Sciences · #Stochastic processes and financial applications #stochastic dynamics and bifurcation #Risk and Portfolio Optimization

paper · doi:10.1137/120902318

Abstract

A version of the fundamental mean-square convergence theorem is proved for stochastic differential equations (SDEs) in which coefficients are allowed to grow polynomially at infinity and which satisfy a one-sided Lipschitz condition. The theorem is illustrated on a number of particular numerical methods, including a special balanced scheme and fully implicit methods. The proposed special balanced scheme is explicit and its mean-square order of convergence is 1/2. Some numerical tests are presented.

Citations

• Numerical Methods for Stochastic Systems Preserving Symplectic Structure

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