Euler-Maruyama
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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Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients
... The rest of the paper is arranged as follows. In section 2, we introduce the monotone condition under which we prove the existence of a unique solution to equation (1.1), along with appropriate bounds that will be needed ...
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Exponential stability of the Euler-Maruyama method for neutral stochastic functional differential equations with jumps
... Abstract The exponential stability of trivial solution and the numerical solution for neutral stochastic func- tional differential equations (NSFDEs) with jumps is considered. The stability includes the almost sure expo- ...
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Multi-level Monte Carlo methods with the truncated Euler-Maruyama scheme for stochastic differential equations
... 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 differential equations ...
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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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Almost sure stability of the Euler-Maruyama method with random variable stepsize for stochastic differential equations
... the Euler-Maruyama method, may reproduce the almost sure stability of SDEs with the global Lipschitz coefficients, but the requirements on the time stepsize are very ...the Euler- Maruyama ...
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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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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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The truncated Euler–Maruyama method for stochastic differential equations
... the Euler-Maruyama (EM) or the stochastic theta method satisfy the moment bounded condition, and hence they proved that the numerical solutions converge to the exact solution in the strong sense under the ...
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The truncated Euler-Maruyama method for stochastic differential delay equations
... On the other hand, there are in general no explicit solutions to nonlinear SDDEs, whence numerical solutions are required in practice. The numerical solutions under the linear growth condition plus the local Lipschitz ...
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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
... However, γ > 1 implies that the diffusion coefficient does not satisfy the linear growth condition so we cannot apply the classical results (e.g. [9]) on the existence and unique- ness of the solutions, boundedness of ...
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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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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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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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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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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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Numerical solutions of neutral stochastic functional differential equations
... In section 2, we introduce some necessary assumptions and auxiliary results, de- fine the Euler–Maruyama method for NSFDEs and state our main result that the approximate solutions strongly converge to the ...
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An introduction to multilevel Monte Carlo for option valuation
... Now, we may view Monte Carlo as requiring a “black box” that returns independent samples. In our numerical SDE context, the samples come from a distribution that is only approximately correct, and the black box (the ...
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