Cumulant approach of arbitrary truncated Levy flight

Vinogradov, D. V.

doi:10.1016/j.physa.2010.09.014

Cited by 8 publications

(15 citation statements)

References 14 publications

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“…random walk processes. In article [13], the cumulants of symmetrical arbitrary truncated Levy flight were reported. Here, the cumulants of arbitrary asymmetrically truncated Levy flight have been obtained.…”

Section: Discussionmentioning

confidence: 99%

“…Notwithstanding the fact that truncated Levy flights have received wide acceptance for the description of financial stochastic processes in econophysics, research focusing on the influence of the deformation shape on the stochastic process characteristics has only recently been carried out [13]. The problem of an arbitrary truncated Levy flight description using the cumulant approach has been solved for an approximation of a one-dimensional probability distribution function (pdf).…”

Section: Introductionmentioning

confidence: 99%

“…This article is a continuation of article [13] and has two goals. The first goal is to show the possibilities and advantages of the generalized correlation function approach with regard to the description of a typical stochastic financial process model.…”

Section: Introductionmentioning

confidence: 99%

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Arbitrary truncated Levy flight: Asymmetrical truncation and high-order correlations

Vinogradov¹

2012

Physica A: Statistical Mechanics and its Applications

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Abstract.The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically distributed increments in the general case, and high-order correlations have been investigated. The cumulants of an asymmetrically truncated Levy distribution have been found. The behaviors of asymmetrically truncated Levy flight, as a particular case of a random walk, are considered. It is shown that, in the Levy regime, high-order correlations between values of asymmetrically truncated Levy flight exist. The source of high-order correlations is the non-Gaussianity of the increments: the increment skewness generates threefold correlation, and the increment kurtosis generates fourfold correlation.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Arbitrary truncated Levy flight: Asymmetrical truncation and high-order correlations

Vinogradov¹

2012

Physica A: Statistical Mechanics and its Applications

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“…Baeumer and Meerschaert 10 used exponential tempering to cool the large power‐law jumps in the modeling of anomalous super diffusion. Authors also used exponential tempering in the probability distribution of waiting times which led to the tempered stable Lévy process having finite moments 2,11 …”

Section: Introductionmentioning

confidence: 99%

Numerical approximation of tempered fractional Sturm‐Liouville problem with application in fractional diffusion equation

Yadav

Pandey

2020

Numerical Methods in Fluids

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Summary In this paper, we discuss the numerical approximation to solve regular tempered fractional Sturm‐Liouville problem (TFSLP) using finite difference method. The tempered fractional differential operators considered here are of Caputo type. The numerically obtained eigenvalues are real, and the corresponding eigenfunctions are orthogonal. The obtained eigenfunctions work as basis functions of weighted Lebesgue integrable function space Lw2 (a,b). Further, the obtained eigenvalues and corresponding eigenfunctions are used to provide weak solution of the tempered fractional diffusion equation. Approximation and error bounds of the solution of the tempered fractional diffusion equation are provided.

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“…Multi-scaling properties of truncated Lévy flights was investigated by Nakao [30] for the first time. Arbitrary truncation of Lévy flights was considered in Vinogradov [37]. In Figueiredo et al [14], truncated Lévy flights are extended to possess autocorrelation, which is often observed in the real-world financial data.…”

Section: Introductionmentioning

confidence: 99%

On finite truncation of infinite shot noise series representation of tempered stable laws

Imai

Kawai

2011

Physica A: Statistical Mechanics and its Applications

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Tempered stable processes are widely used in various fields of application as alternatives with finite second moment and long-range Gaussian behaviors to stable processes. Infinite shot noise series representation is the only exact simulation method for the tempered stable process and has recently attracted attention for simulation use with ever improved computational speed. In this paper, we derive series representations for the tempered stable laws of increasing practical interest through the thinning, rejection, and inverse Lévy measure methods. We make a rigorous comparison among those representations, including the existing one due to [18, 34], in terms of the tail mass of Lévy measures which can be simulated under a common finite truncation scheme. The tail mass are derived in closed form for some representations thanks to various structural properties of the tempered stable laws. We prove that the representation via the inverse Lévy measure method achieves a much faster convergence in truncation to the infinite sum than all the other representations. Numerical results are presented to support our theoretical analysis.

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Cumulant approach of arbitrary truncated Levy flight

Cited by 8 publications

References 14 publications

Arbitrary truncated Levy flight: Asymmetrical truncation and high-order correlations

Arbitrary truncated Levy flight: Asymmetrical truncation and high-order correlations

Numerical approximation of tempered fractional Sturm‐Liouville problem with application in fractional diffusion equation

On finite truncation of infinite shot noise series representation of tempered stable laws

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