A Legendre-based computational method for solving a class of Itô stochastic delay differential equations

Ernst, Philip; Soleymani, Fazlollah

doi:10.1007/s11075-018-0526-y

Cited by 8 publications

(2 citation statements)

References 22 publications

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“…The main advantage of this numerical scheme is that, convergence analysis can be provided in the best manner, meanwhile direct collocation methods have some difficulties to provide their convergence analysis. Moreover, the suggested scheme (i.e., LGCM) is easy to perform and could be applied for solving variable order fractional multi-Pantograph BVPs (Jia et al 2017;Wu 2015, 2017), delay fractional optimal control problems (Hosseinpour et al 2019), delay partial differential equations (Hosseinpour et al 2018) and stochastic delay differential equations (Ernst and Soleymani 2019). However, some modifications should be Fig.…”

Section: Discussionmentioning

confidence: 99%

Numerical solution of multi-Pantograph delay boundary value problems via an efficient approach with the convergence analysis

Yang

Tohidi

2019

Comp. Appl. Math.

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This present investigation is contemplated to provide Legendre spectral collocation method for solving multi-Pantograph delay boundary value problems (BVPs). In this regard, an equivalent integral form of such BVPs has been considered. The proposed method is based on Legendre-Gauss collocation nodes and Legendre-Gauss quadrature rule. Convergence analysis associated to the presented scheme has been provided to show its applicability theoretically. Some numerical examples are given to demonstrate the efficiency, accuracy, and versatility of our method. Numerical results confirm the theoretical predictions and are superior with respect to several recent numerical methods including Hermite collocation approach, Laguerre collocation technique and the reproducing kernel method.

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Section: Discussionmentioning

confidence: 99%

Numerical solution of multi-Pantograph delay boundary value problems via an efficient approach with the convergence analysis

Yang

Tohidi

2019

Comp. Appl. Math.

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“…In fact, the difference between two independent identically distributed exponential random variables is controlled by a Laplace distribution, as is a Brownian motion computed at an exponentially distributed random time. This distribution is employable in situations wherein the lower values originate under different external conditions than the higher ones such that they follow a different pattern, see [11,12] for further discussions.…”

Section: Laplace Distributionmentioning

confidence: 99%

Revisiting the Copula-Based Trading Method Using the Laplace Marginal Distribution Function

2022

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Pairs trading under the copula approach is revisited in this paper. It is well known that financial returns arising from indices in markets may not follow the features of normal distribution and may exhibit asymmetry or fatter tails, in particular. Due to this, the Laplace distribution is employed in this work to fit the marginal distribution function, which will then be employed in a copula function. In fact, a multivariate copula function is constructed on two indices (based on the Laplace marginal distribution), enabling us to obtain the associated probabilities required for the process of pairs trade and creating an efficient tool for trading.

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Numerical solution of Itô-Volterra integral equation by least squares method

Ahmadinia

Heydari

2019

Numer Algor

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A Legendre-based computational method for solving a class of Itô stochastic delay differential equations

Cited by 8 publications

References 22 publications

Numerical solution of multi-Pantograph delay boundary value problems via an efficient approach with the convergence analysis

Numerical solution of multi-Pantograph delay boundary value problems via an efficient approach with the convergence analysis

Revisiting the Copula-Based Trading Method Using the Laplace Marginal Distribution Function

Numerical solution of Itô-Volterra integral equation by least squares method

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