euler-maruyama (EM)
Almost sure exponential stability of backward Euler–Maruyama discretizations for hybrid stochastic differential equations
... This is a continuation of the first author’s earlier paper [17] jointly with Pang and Deng, in which the authors established some sufficient conditions under which the Euler–Maruyama (EM) method can ...
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Almost sure exponential stability of the Euler–Maruyama approximations for stochastic functional differential equations
... the Euler–Maruyama (EM) approxi- mations of stochastic functional differential equations (SFDEs) can share the almost sure exponential stability of the exact ...
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Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps
... NSFDEs with Poisson jumps are an important type of stochastic system model, and their stability analysis has attracted considerable attention in recent years. Since most stochastic systems cannot be solved explicitly, ...
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Almost sure stability of the Euler-Maruyama method with random variable stepsize for stochastic differential equations
... Bearing those points above in mind, the random variable stepsize is introduced to embed into the classic Euler-Maruyama (EM) method in this paper. Our key contribution is that we prove the time variable is ...
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Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients
... It is now clear that to prove the strong convergence theorem under condition (1.2) it is necessary to modify the EM scheme. Motivated by the existing works [18] and [21] we consider implicit schemes. These authors have ...
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Discrete Razumikhin-type technique and stability of the Euler-Maruyama method to stochastic functional differential equations
... the Euler–Maruyama (EM) scheme can reproduce the mo- ment exponential stability of exact solutions of stochastic functional differen- tial equations ...
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Convergence rate and stability of the truncated Euler-Maruyama method for stochastic differential equations
... classical Euler–Maruyama (EM) method is convenient for computations and implementations, the absolute moments of its approximation for SDEs with super-linear coefficients diverge to infinite at a finite ...
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Convergence rates of the truncated Euler-Maruyama method for stochastic differential equations
... Influenced by Higham, Mao and Stuart [9], several numerical methods have been de- veloped to study the strong convergence of the numerical solutions to stochastic differen- tial equations (SDEs) under the local Lipschitz ...
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A highly sensitive mean-reverting process in finance and the Euler-Maruyama approximations
... This section deals with the regime where the time interval, [0, T ], is fixed. There is so far no explicit solution to Eq. (2.1) so we consider its numerical solution. We refer to it as the Euler–Maruyama ...
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The truncated Euler–Maruyama method for stochastic differential equations
... Influenced by Higham, Mao and Stuart [10], several numerical methods have been developed to study the strong convergence of the numerical solutions to stochas- tic differential equations (SDEs) under the local Lipschitz ...
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The truncated Euler-Maruyama method for stochastic differential delay equations
... Abstract The numerical solutions of stochastic differential delay equations (SDDEs) under the generalized Khasminskii-type condition were discussed by Mao (Appl. Math. Comput. 217, 5512–5524 2011), and the theory there ...
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Equivalence of the mean square stability between the partially truncated Euler–Maruyama method and stochastic differential equations with super linear growing coefficients
... Since then, many works have been devoted to the study on the equivalence of the mean square stability between different types of SDEs and their numerical methods. The author in [18] investigated the stochastic differential ...
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Multi-level Monte Carlo methods with the truncated Euler-Maruyama scheme for stochastic differential equations
... tamed Euler method and the tamed Milstein method can be found in [27] and [30], ...truncated Euler–Maruyama (EM) method was developed in [21,22], which is also targeting on SDEs with non-global ...
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On One Step Method of Euler Maruyama Type for Solution of Stochastic Differential Equations Using Varying Stepsizes
... one-step Euler-Maruyama method (EMM) for solution of SDE (3) and apply it to solve two problems in the form of first order ...one-step Euler-Maruyama ...
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Almost sure and moment exponential stability of Euler-Maruyama discretizations for hybrid stochastic differential equations
... the Euler–Maruyama can match the stability properties of a single linear SDE for sufficiently small ∆ > 0, it is much more demanding to ask a method to maintain this behaviour over all possible averages, ...
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Asymptotic boundedness and stability of solutions to hybrid stochastic differential equations with jumps and the Euler-Maruyama approximation
... 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] ...
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The partially truncated Euler-Maruyama method and its stability and boundedness
... We will not only establish the finite-time strong Lr -convergence theory for the partially truncated EM method, but also demonstrate the real benefit of the method by showing that the me[r] ...
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A note on the partially truncated Euler–Maruyama method
... 2 Motivation In this section, we will point out that one condition imposed in [3] is restrictive in the sense that this condition might force the stepsize to be so small that the partial[r] ...
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Numerical stationary distribution and its convergence for nonlinear stochastic differential equations
... The second author’s series papers [21, 33, 31] are devoted to numerical sta- tionary distributions of stochastic differential equations. In those series papers, the explicit Euler–Maruyama (EM) method was ...
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An introduction to multilevel Monte Carlo for option valuation
... Giles [16] has also shown how to construct estimators for which β > γ = 1, by replacing Euler–Maruyama with the more strongly accurate Milstein scheme. For European-style options with Lipschitz payoff ...
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