Approximation of the first passage time distribution for the birth–death processes

Kononovičius, Aleksejus; Gontis, Vygintas

doi:10.1088/1742-5468/ab2709

Cited by 6 publications

(7 citation statements)

References 52 publications

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“…We will call this problem the chemical birth-death process to distinguish it from the many other birthdeath processes that have been considered in the literature, e.g [19,20,21]…”

mentioning

confidence: 99%

The chemical birth-death process with additive noise

Vastola¹

2019

Preprint

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The chemical birth-death process, whose chemical master equation (CME) is exactly solvable, is a paradigmatic toy problem often used to get intuition for how stochasticity affects chemical kinetics. In a certain limit, it can be approximated by an Ornstein-Uhlenbeck-like process which is also exactly solvable. In this paper, we use this system to showcase eight qualitatively different ways to exactly solve continuous stochastic systems: (i) integrating the stochastic differential equation; (ii) computing the characteristic function; (iii) eigenfunction expansion; (iv) using ladder operators; (v) the Martin-Siggia-Rose-Janssen-De Dominicis path integral; (vi) the Onsager-Machlup path integral; (vii) semiclassically approximating the Onsager-Machlup path integral; and (viii) approximating the solution to the corresponding CME.

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“…We will call this problem the chemical birth-death process to distinguish it from the many other birthdeath processes that have been considered in the literature, e.g [19,20,21]…”

mentioning

confidence: 99%

The chemical birth-death process with additive noise

Vastola¹

2019

Preprint

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“…Our expectation that burst and inter-burst duration analysis can give an additional value in the estimation of long-range memory property is based on the previous study of the first passage time problem in birth-death processes and the duration PDF in-variance regarding non-linear transformations of the time series [22,24,34,41,43]. This empirical analysis of LOB data strengthens our expectation providing evidence that the definition of Hurst exponent using burst and inter-burst duration analysis can be more reliable in comparison with other widely used methods.…”

Section: Discussionmentioning

confidence: 99%

Long-range memory test by the burst and inter-burst duration distribution

Gontis

2020

Preprint

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It is empirically established that order flow in the financial markets is positively auto-correlated and can serve as an example of a social system with long-range memory. Nevertheless, widely used long-range memory estimators give varying values of the Hurst exponent. We propose the burst and inter-burst duration statistical analysis as one more test of long-range memory and implement it with the limit order book data comparing it with other widely used estimators. This method gives a more reliable evaluation of the Hurst exponent independent of the stock in consideration or time definition used. Results strengthen the expectation that burst and inter-burst duration analysis can serve as a better method to investigate the property of long-range memory.

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“…We proposed a test earlier, based on the specific first-passage times, which we refer to as the burst and interburst duration analysis (abbr. BDA) [ 148 , 149 , 150 , 151 ].…”

Section: Searching For the True Long-range Memory Testmentioning

confidence: 99%

“…One has to take into account the interplay of endogenous and exogenous fluctuations in the financial markets to build a comprehensive model of this complex system [ 154 ]. Non-linear SDEs might be applicable in the modeling of other social systems, where models of opinion or population dynamics lead to the macroscopic description by these equations [ 148 , 149 , 150 , 151 ]. The description by SDEs is an alternative to the modeling incorporating fractional dynamics, if power–law statistical properties are observed in the empirical data.…”

Section: Searching For the True Long-range Memory Testmentioning

confidence: 99%

“…The first component is a statistical test, which should distinguish between spurious and true long-range memory. Currently, we are considering the BDA method [ 148 , 149 , 150 , 151 ], which performs reasonably well in comparison to the alternatives. The core idea of the method is that for any one-dimensional Markovian random walk first-passage time PDF should be a power–law with exponent

at least for some of the duration.…”

Section: Future Considerationsmentioning

confidence: 99%

See 1 more Smart Citation

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

Kazakevičius

Kononovičius

Kaulakys

et al. 2021

Entropy

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In the face of the upcoming 30th anniversary of econophysics, we review our contributions and other related works on the modeling of the long-range memory phenomenon in physical, economic, and other social complex systems. Our group has shown that the long-range memory phenomenon can be reproduced using various Markov processes, such as point processes, stochastic differential equations, and agent-based models—reproduced well enough to match other statistical properties of the financial markets, such as return and trading activity distributions and first-passage time distributions. Research has lead us to question whether the observed long-range memory is a result of the actual long-range memory process or just a consequence of the non-linearity of Markov processes. As our most recent result, we discuss the long-range memory of the order flow data in the financial markets and other social systems from the perspective of the fractional Lèvy stable motion. We test widely used long-range memory estimators on discrete fractional Lèvy stable motion represented by the auto-regressive fractionally integrated moving average (ARFIMA) sample series. Our newly obtained results seem to indicate that new estimators of self-similarity and long-range memory for analyzing systems with non-Gaussian distributions have to be developed.

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Approximation of the first passage time distribution for the birth–death processes

Cited by 6 publications

References 52 publications

The chemical birth-death process with additive noise

The chemical birth-death process with additive noise

Long-range memory test by the burst and inter-burst duration distribution

Understanding the Nature of the Long-Range Memory Phenomenon in Socioeconomic Systems

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