[PDF] Top 20 Convergence rates of the truncated Euler-Maruyama method for stochastic differential equations

... strong convergence question for numerical approximations under the local Lipschitz ...of convergence, say weak convergence, convergence in probability and pathwise convergence, are ... See full document

... simulations. Convergence and stability of these methods are well understood for SDEs with Lipschitz continuous coefficients: see [26] for ...strong convergence and stability questions for numerical ... See full document

... Actually, many interesting works have been devoted to (A), i.e., given the SDE is stable under certain conditions, some numerical method can reproduce such a stability. We just mention some of the works here [2, ... See full document

... be arbitrarily close to q / 2 under some additional conditions. However, there are some restrictions on the truncation functions and these restrictions sometimes might force the step size to be so small that the ... See full document

... EM method has its simple algebraic structure, cheap com- putational cost and acceptable convergence rate under the global Lipschitz condition, it has been attracting lots of attention ...EM method ... See full document

... the truncated Euler–Maruyama method developed in Mao (2015), we propose the truncated Milstein method in this ...strong convergence rate is proved to be close to 1 for a ... See full document

... the Euler scheme, by analyzing the numerical convergence rates based on a reference ...of convergence heavily depends on the initial value and properties of the drift coefficient, ...numerical ... See full document

... The truncated Euler–Maruyama method is employed together with the Multi-level Monte Carlo method to approximate expectations of some func- tions of solutions to stochastic ... See full document

... condition. In 2002, Mao [14] generalized the the well-known Khasminskii test [7] from stochastic differential equations (SDEs) to SDDEs. The Khasminskii-type the- orem established in [14] for SDDEs ... See full document

... In [31], the authors provided the following three assumptions and proved that under those assumptions the Euler–Maruyama solution of the stochastic dif- ferential equation has a unique stationary ... See full document

... Let us now return to the SDE (3.1). In Section 3 we have shown that the EM method cannot reproduce the almost sure exponential stability of the SDE. However, our the- ory established in the previous sections shows ... See full document

... for stochastic differential equations (SDEs) has recently received a more and more ...ordinary differential equations (ODEs) is motivated by the question “for what choices of stepsize ... See full document

... In finance and economics, in order to obtain the dynamics observed, it is important to model the impact of event-driven uncertainty. Events such as corporate defaults, opera- tional failures, market crashes or central ... See full document

... 12 4 5 6 7 8 9 10 13 14 15 16 17 Convergence analysis of the EM approximate solutions In this section, we will study the convergence of the EM approximate solutions for hybrid SDEs with [r] ... See full document

... In this subsection, under the same conditions as those in Theorem ., we will obtain the exponential stability in mean square of the exponential Euler method (.) to SLSDDEs (.) in Theorem .. It is ... See full document

... for stochastic volatility involving state-dependent delayed response and applied the Euler–Maruyama discrete-time approximation in the strong convergence sense to simu- ...of stochastic ... See full document

... Recently, stochastic differential equations with jumps (SDEwJs) are becoming increas- ingly used to model real-world phenomena in different fields, such as economics, finance, biology, and ...the ... See full document

... Milstein method and no nonlinear algebra problems are encountered during ...IM method is, to a certain extent, improved even for the non-stiff prob- lem (see Table  in Section ), despite the fact that the ... See full document

... this method in approximating the solution of ...of stochastic Taylor expansions, up to ...the Euler– Maruyama and Milstein schemes had been proposed to apply them in practice or to study their ... See full document

... of stochastic differential delay equations under the generalized Khasminskii-type conditions, Applied Mathematics and Computation, 217(2011), ...Ding, Convergence and stability of Euler ... See full document