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Journal articles on the topic 'Lévy area'

Author: Grafiati

Published: 23 September 2022

Last updated: 31 July 2025

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1

Gottwald, Georg A., and Ian Melbourne. "Time-reversibility and nonvanishing Lévy area." Nonlinearity 37, no. 7 (2024): 075018. http://dx.doi.org/10.1088/1361-6544/ad4947.

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Abstract We give a complete description and clarification of the structure of the Lévy area correction to Itô/Stratonovich stochastic integrals arising as limits of time-reversible deterministic dynamical systems. In particular, we show that time-reversibility forces the Lévy area to vanish only in very specific situations that are easily classified. In the absence of such obstructions, we prove that there are no further restrictions on the Lévy area and that it is typically nonvanishing and far from negligible.

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2

Neuenkirch, A., S. Tindel, and J. Unterberger. "Discretizing the fractional Lévy area." Stochastic Processes and their Applications 120, no. 2 (2010): 223–54. http://dx.doi.org/10.1016/j.spa.2009.10.007.

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3

Li, Juan, Qing An, Hong Lei, Qian Deng, and Gai-Ge Wang. "Survey of Lévy Flight-Based Metaheuristics for Optimization." Mathematics 10, no. 15 (2022): 2785. http://dx.doi.org/10.3390/math10152785.

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Lévy flight is a random walk mechanism which can make large jumps at local locations with a high probability. The probability density distribution of Lévy flight was characterized by sharp peaks, asymmetry, and trailing. Its movement pattern alternated between frequent short-distance jumps and occasional long-distance jumps, which can jump out of local optimal and expand the population search area. The metaheuristic algorithms are inspired by nature and applied to solve NP-hard problems. Lévy flight is used as an operator in the cuckoo algorithm, monarch butterfly optimization, and moth search

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4

Malham, Simon J. A., and Anke Wiese. "Efficient almost-exact Lévy area sampling." Statistics & Probability Letters 88 (May 2014): 50–55. http://dx.doi.org/10.1016/j.spl.2014.01.022.

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5

Ledoux, M., T. Lyons, and Z. Qian. "Lévy area of Wiener processes in Banach spaces." Annals of Probability 30, no. 2 (2002): 546–78. http://dx.doi.org/10.1214/aop/1023481002.

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6

Capitaine, M., and C. Donati-Martin. "The Lévy Area Process for the Free Brownian Motion." Journal of Functional Analysis 179, no. 1 (2001): 153–69. http://dx.doi.org/10.1006/jfan.2000.3679.

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7

Kilic, Ilker. "A Lévy Flight Based BAT Optimization Algorithm for Block-based Image Compression." Tehnički glasnik 16, no. 4 (2022): 477–83. http://dx.doi.org/10.31803/tg-20220329112403.

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Many metaheuristics have been adopted to solve the codebook generation problem in image processing. In this paper, the Bat algorithm is combined by the Lévy flight distribution to find out the global optimum codebook. The Lévy flight distribution is combined by the local search procedure. Therefore most of the time the bat concentrate on the local area for specific food while it rarely flies to the different parts of the field for better food opportunities. This process strongly guides the bat on the global minimum way and offers better food, then the bat flies to that direction. Consequently,

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8

Letemplier, Julien, and Thomas Simon. "The area of a spectrally positive stable process stopped at zero." Probability and Mathematical Statistics 38, no. 1 (2018): 27–37. http://dx.doi.org/10.19195/0208-4147.38.1.2.

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A multiplicative identity in law for the area of a spectrally positive Lévy ∝-stable process stopped at zero is established. Extending that of Lefebvre for Brownian motion, it involves an inverse beta random variable and the square of a positive stable random variable. This simple identity makes it possible to study precisely the behaviour of the density at zero, which is Fréchet-like.

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9

Hills, Thomas T., Christopher Kalff, and Jan M. Wiener. "Adaptive Lévy Processes and Area-Restricted Search in Human Foraging." PLoS ONE 8, no. 4 (2013): e60488. http://dx.doi.org/10.1371/journal.pone.0060488.

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10

Schehr, Grégory, and Satya N. Majumdar. "Area distribution and the average shape of a Lévy bridge." Journal of Statistical Mechanics: Theory and Experiment 2010, no. 08 (2010): P08005. http://dx.doi.org/10.1088/1742-5468/2010/08/p08005.

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11

Levin, Daniel, and Mark Wildon. "A combinatorial method for calculating the moments of Lévy area." Transactions of the American Mathematical Society 360, no. 12 (2008): 6695–709. http://dx.doi.org/10.1090/s0002-9947-08-04526-1.

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12

Wang, Shipeng, Xiaoping Yang, Xingqiao Wang, and Zhihong Qian. "A Virtual Force Algorithm-Lévy-Embedded Grey Wolf Optimization Algorithm for Wireless Sensor Network Coverage Optimization." Sensors 19, no. 12 (2019): 2735. http://dx.doi.org/10.3390/s19122735.

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The random placement of a large-scale sensor network in an outdoor environment often causes low coverage. In order to effectively improve the coverage of a wireless sensor network in the monitoring area, a coverage optimization algorithm for wireless sensor networks with a Virtual Force-Lévy-embedded Grey Wolf Optimization (VFLGWO) algorithm is proposed. The simulation results show that the VFLGWO algorithm has a better optimization effect on the coverage rate, uniformity, and average moving distance of sensor nodes than a wireless sensor network coverage optimization algorithm using Lévy-embe

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13

Ferreiro-Castilla, Albert, and Frederic Utzet. "Lévy area for Gaussian processes: A double Wiener–Itô integral approach." Statistics & Probability Letters 81, no. 9 (2011): 1380–91. http://dx.doi.org/10.1016/j.spl.2011.04.015.

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14

Kuelbs, James, and Wenbo Li. "A Functional LIL for Stochastic Integrals and the Lévy Area Process." Journal of Theoretical Probability 18, no. 2 (2005): 261–90. http://dx.doi.org/10.1007/s10959-003-2604-9.

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15

Diamantakis, Theo, Darryl D. Holm, and Grigorios A. Pavliotis. "Variational Principles on Geometric Rough Paths and the Lévy Area Correction." SIAM Journal on Applied Dynamical Systems 22, no. 2 (2023): 1182–218. http://dx.doi.org/10.1137/22m1522164.

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16

Li, Juan, Yuan-Hua Yang, Qing An, Hong Lei, Qian Deng, and Gai-Ge Wang. "Moth Search: Variants, Hybrids, and Applications." Mathematics 10, no. 21 (2022): 4162. http://dx.doi.org/10.3390/math10214162.

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Moth search (MS) is a nature-inspired metaheuristic optimization algorithm based on the most representative characteristics of moths, Lévy flights and phototaxis. Phototaxis signifies a movement which organism towards or away from a source of light, which is the representative features for moths. The best moth individual is seen as the light source in Moth search. The moths that have a smaller distance from the best one will fly around the best individual by Lévy flights. For reasons of phototaxis, the moths, far from the fittest one, will fly towards the best one with a big step. These two fe

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17

Duncan, S., G. Estrada-Rodriguez, J. Stocek, M. Dragone, P. A. Vargas, and H. Gimperlein. "Efficient quantitative assessment of robot swarms: coverage and targeting Lévy strategies." Bioinspiration & Biomimetics 17, no. 3 (2022): 036006. http://dx.doi.org/10.1088/1748-3190/ac57f0.

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Abstract Biologically inspired strategies have long been adapted to swarm robotic systems, including biased random walks, reaction to chemotactic cues and long-range coordination. In this paper we apply analysis tools developed for modeling biological systems, such as continuum descriptions, to the efficient quantitative characterization of robot swarms. As an illustration, both Brownian and Lévy strategies with a characteristic long-range movement are discussed. As a result we obtain computationally fast methods for the optimization of robot movement laws to achieve a prescribed collective be

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18

Hudson, Robin, and Yuchen Pei. "On a causal quantum stochastic double product integral related to Lévy area." Annales de l’Institut Henri Poincaré D 5, no. 4 (2018): 467–512. http://dx.doi.org/10.4171/aihpd/60.

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19

Blanchet, J., and M. Mandjes. "Asymptotics of the area under the graph of a Lévy-driven workload process." Operations Research Letters 41, no. 6 (2013): 730–36. http://dx.doi.org/10.1016/j.orl.2013.10.004.

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20

Bonnefont, Michel, and Nicolas Juillet. "Couplings in $L^{p}$ distance of two Brownian motions and their Lévy area." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 56, no. 1 (2020): 543–65. http://dx.doi.org/10.1214/19-aihp972.

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21

Giles, Michael B., and Lukasz Szpruch. "Antithetic multilevel Monte Carlo estimation for multi-dimensional SDEs without Lévy area simulation." Annals of Applied Probability 24, no. 4 (2014): 1585–620. http://dx.doi.org/10.1214/13-aap957.

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22

Yamada, Toshihiro, and Kenta Yamamoto. "A second-order weak approximation of SDEs using a Markov chain without Lévy area simulation." Monte Carlo Methods and Applications 24, no. 4 (2018): 289–308. http://dx.doi.org/10.1515/mcma-2018-2024.

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Abstract This paper proposes a new Markov chain approach to second-order weak approximations of stochastic differential equations (SDEs) driven by d-dimensional Brownian motion. The scheme is explicitly constructed by polynomials of Brownian motions up to second order, and any discrete moment-matched random variables or the Lévy area simulation method are not used. The required number of random variables is still d in one-step simulation of the implementation of the scheme. In the Markov chain, a correction term with Lie bracket of vector fields associated with SDEs appears as the cost of not

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23

Chen, Pengyu, Hua Yue, Xiaobo Zhai, et al. "Transport of a graphene nanosheet sandwiched inside cell membranes." Science Advances 5, no. 6 (2019): eaaw3192. http://dx.doi.org/10.1126/sciadv.aaw3192.

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The transport of nanoparticles at bio-nano interfaces is essential for many cellular responses and biomedical applications. How two-dimensional nanomaterials, such as graphene and transition-metal dichalcogenides, diffuse along the cell membrane is, however, unknown, posing an urgent and important issue to promote their applications in the biomedical area. Here, we show that the transport of graphene oxides (GOs) sandwiched inside cell membranes varies from Brownian to Lévy and even directional dynamics. Specifically, experiments evidence sandwiched graphene–cell membrane superstructures in di

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24

Abundo, Mario, and Sara Furia. "Joint Distribution of First-Passage Time and First-Passage Area of Certain Lévy Processes." Methodology and Computing in Applied Probability 21, no. 4 (2018): 1283–302. http://dx.doi.org/10.1007/s11009-018-9677-5.

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25

El-Hadidy, Mohamed Abd Allah. "Study of water pollution through a Lévy flight jump diffusion model with stochastic jumps of pollutants." International Journal of Modern Physics B 33, no. 19 (2019): 1950210. http://dx.doi.org/10.1142/s0217979219502102.

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In this paper, we present the multivariate distribution of independent Lévy flight jump diffusion molecules that cause water pollution. We consider that the waiting time of this jump has a Gaussian distribution. Rather than studying the statistical properties of this distribution in water, we estimate the length of the jump distance parameters for each molecule. These estimated jump distances of the molecules are used to predict the proportion of pollution in a large area of the sea.

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26

Gunavathi, Chellamuthu, and Kandasamy Premalatha. "A Comparative Analysis of Swarm Intelligence Techniques for Feature Selection in Cancer Classification." Scientific World Journal 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/693831.

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Feature selection in cancer classification is a central area of research in the field of bioinformatics and used to select the informative genes from thousands of genes of the microarray. The genes are ranked based onT-statistics, signal-to-noise ratio (SNR), andF-test values. The swarm intelligence (SI) technique finds the informative genes from the top-m ranked genes. These selected genes are used for classification. In this paper the shuffled frog leaping with Lévy flight (SFLLF) is proposed for feature selection. In SFLLF, the Lévy flight is included to avoid premature convergence of shuff

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27

Liu, Lixing, Hongjie Liu, Jianping Li, Pengfei Wang, and Xin Yang. "Construction of Orchard Agricultural Machinery Dispatching Model Based on Improved Beetle Optimization Algorithm." Agronomy 15, no. 2 (2025): 323. https://doi.org/10.3390/agronomy15020323.

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In order to enhance orchard agricultural efficiency and lower fruit production expenses, we propose a BL-DBO (Beetle Optimization Algorithm introducing Bernoulli mapping and Lévy flights) to solve the agricultural machinery dispatching model within the orchard area. First, we analyze the agricultural machinery dispatching problem in the orchard area and establish its mathematical model with the objective of minimizing dispatching costs as a constraint. To tackle the problems of uneven individual position distribution and the risk of becoming stuck in local optimal solutions in the traditional

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28

Qian, Zhongmin, and Xingcheng Xu. "Lévy area analysis and parameter estimation for fOU processes via non-geometric rough path theory." Acta Mathematica Scientia 44, no. 5 (2024): 1609–38. http://dx.doi.org/10.1007/s10473-024-0501-8.

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29

Lopusanschi, Olga, and Damien Simon. "Lévy area with a drift as a renormalization limit of Markov chains on periodic graphs." Stochastic Processes and their Applications 128, no. 7 (2018): 2404–26. http://dx.doi.org/10.1016/j.spa.2017.09.004.

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30

Deya, A., A. Neuenkirch, and S. Tindel. "A Milstein-type scheme without Lévy area terms for SDEs driven by fractional Brownian motion." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 48, no. 2 (2012): 518–50. http://dx.doi.org/10.1214/10-aihp392.

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31

Bennison, Ashley, John L. Quinn, Alison Debney, and Mark Jessopp. "Tidal drift removes the need for area-restricted search in foraging Atlantic puffins." Biology Letters 15, no. 7 (2019): 20190208. http://dx.doi.org/10.1098/rsbl.2019.0208.

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Understanding how animals forage is a central objective in ecology. Theory suggests that where food is uniformly distributed, Brownian movement ensures the maximum prey encounter rate, but when prey is patchy, the optimal strategy resembles a Lévy walk where area-restricted search (ARS) is interspersed with commuting between prey patches. Such movement appears ubiquitous in high trophic-level marine predators. Here, we report foraging and diving behaviour in a seabird with a high cost of flight, the Atlantic puffin ( Fratercula arctica ), and report a clear lack of Brownian or Levy flight and

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32

Pang, Bao, Yong Song, Chengjin Zhang, Hongling Wang, and Runtao Yang. "A Swarm Robotic Exploration Strategy Based on an Improved Random Walk Method." Journal of Robotics 2019 (March 13, 2019): 1–9. http://dx.doi.org/10.1155/2019/6914212.

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An environment can be searched far more efficiently if the appropriate search strategy is used. Because of the limited individual abilities of swarm robots, namely, local sensing and low processing power, random searching is the main search strategy used in swarm robotics. The random walk methods that are used most commonly are Brownian motion and Lévy flight, both of which mimic the self-organized behavior of social insects. However, both methods are somewhat limited when applied to swarm robotics, where having the robots search repeatedly can result in highly inefficient searching. Therefore

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33

Maletz, Jörg. "Arenig biostratigraphy of the Pointe-de-Lévy slice, Quebec Appalachians, Canada." Canadian Journal of Earth Sciences 34, no. 6 (1997): 733–52. http://dx.doi.org/10.1139/e17-061.

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The Pointe-de-Lévy slice includes a nearly complete Arenig graptolite succession. A conspicuous gap exists in the Yapeenian (Ya) to lower Darriwilian (Da) part (Ya 1 – Da 1). The lithological column is compiled from several sections at Lévis, Quebec, that yield only parts of the complete succession. The graptolite zonation can be compared closely with that from the Cow Head Group of western Newfoundland and the Deep Kill Formation of eastern New York. The Shumardia "Limestone" is differentiated into four graptolite zones and subzones, of which the youngest zone clearly belongs to the Llanvirn.

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34

Ekinci, Serdar, Erdal Eker, Davut Izci, Aseel Smerat, and Laith Abualigah. "Enhanced RSA Optimized TID Controller for Frequency Stabilization in a Two-Area Power System." International Journal of Robotics and Control Systems 4, no. 4 (2024): 1886–902. https://doi.org/10.31763/ijrcs.v4i4.1644.

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This study presents an enhanced reptile search algorithm (ImRSA) optimized tilt-integral-derivative (TID) controller for load frequency control (LFC) in a two-area power system consisting of photovoltaic (PV) and thermal power units. The ImRSA integrates Lévy flight and logarithmic spiral search mechanisms to improve the balance between exploration and exploitation, resulting in more efficient optimization performance. The proposed controller is tested against the original reptile search algorithm (RSA) and other state-of-the-art optimization methods, such as modified grey wolf optimization wi

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35

Li, Desheng. "Cooperative Quantum-Behaved Particle Swarm Optimization with Dynamic Varying Search Areas and Lévy Flight Disturbance." Scientific World Journal 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/370691.

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This paper proposes a novel variant of cooperative quantum-behaved particle swarm optimization (CQPSO) algorithm with two mechanisms to reduce the search space and avoid the stagnation, called CQPSO-DVSA-LFD. One mechanism is called Dynamic Varying Search Area (DVSA), which takes charge of limiting the ranges of particles’ activity into a reduced area. On the other hand, in order to escape the local optima, Lévy flights are used to generate the stochastic disturbance in the movement of particles. To test the performance of CQPSO-DVSA-LFD, numerical experiments are conducted to compare the prop

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36

Lundy, Mathieu G., Alan Harrison, Daniel J. Buckley, et al. "Prey field switching based on preferential behaviour can induce Lévy flights." Journal of The Royal Society Interface 10, no. 78 (2013): 20120489. http://dx.doi.org/10.1098/rsif.2012.0489.

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Using the foraging movements of an insectivorous bat, Myotis mystacinus , we describe temporal switching of foraging behaviour in response to resource availability. These observations conform to predictions of optimized search under the Lévy flight paradigm. However, we suggest that this occurs as a result of a preference behaviour and knowledge of resource distribution. Preferential behaviour and knowledge of a familiar area generate distinct movement patterns as resource availability changes on short temporal scales. The behavioural response of predators to changes in prey fields can elicit

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37

Lundy, Mathieu G., Alan Harrison, Daniel J. Buckley, et al. "Prey field switching based on preferential behaviour can induce Lévy flights." Journal of The Royal Society Interface 10, no. 78 (2013): 20120489. https://doi.org/10.5281/zenodo.13450094.

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(Uploaded by Plazi for the Bat Literature Project) Using the foraging movements of an insectivorous bat, Myotis mystacinus , we describe temporal switching of foraging behaviour in response to resource availability. These observations conform to predictions of optimized search under the Lévy flight paradigm. However, we suggest that this occurs as a result of a preference behaviour and knowledge of resource distribution. Preferential behaviour and knowledge of a familiar area generate distinct movement patterns as resource availability changes on short temporal scales. The behavioural response

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38

Lundy, Mathieu G., Alan Harrison, Daniel J. Buckley, et al. "Prey field switching based on preferential behaviour can induce Lévy flights." Journal of The Royal Society Interface 10, no. 78 (2013): 20120489. https://doi.org/10.5281/zenodo.13450094.

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(Uploaded by Plazi for the Bat Literature Project) Using the foraging movements of an insectivorous bat, Myotis mystacinus , we describe temporal switching of foraging behaviour in response to resource availability. These observations conform to predictions of optimized search under the Lévy flight paradigm. However, we suggest that this occurs as a result of a preference behaviour and knowledge of resource distribution. Preferential behaviour and knowledge of a familiar area generate distinct movement patterns as resource availability changes on short temporal scales. The behavioural response

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39

Lundy, Mathieu G., Alan Harrison, Daniel J. Buckley, et al. "Prey field switching based on preferential behaviour can induce Lévy flights." Journal of The Royal Society Interface 10, no. 78 (2013): 20120489. https://doi.org/10.5281/zenodo.13450094.

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(Uploaded by Plazi for the Bat Literature Project) Using the foraging movements of an insectivorous bat, Myotis mystacinus , we describe temporal switching of foraging behaviour in response to resource availability. These observations conform to predictions of optimized search under the Lévy flight paradigm. However, we suggest that this occurs as a result of a preference behaviour and knowledge of resource distribution. Preferential behaviour and knowledge of a familiar area generate distinct movement patterns as resource availability changes on short temporal scales. The behavioural response

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40

Lundy, Mathieu G., Alan Harrison, Daniel J. Buckley, et al. "Prey field switching based on preferential behaviour can induce Lévy flights." Journal of The Royal Society Interface 10, no. 78 (2013): 20120489. https://doi.org/10.5281/zenodo.13450094.

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Abstract:

(Uploaded by Plazi for the Bat Literature Project) Using the foraging movements of an insectivorous bat, Myotis mystacinus , we describe temporal switching of foraging behaviour in response to resource availability. These observations conform to predictions of optimized search under the Lévy flight paradigm. However, we suggest that this occurs as a result of a preference behaviour and knowledge of resource distribution. Preferential behaviour and knowledge of a familiar area generate distinct movement patterns as resource availability changes on short temporal scales. The behavioural response

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41

Lundy, Mathieu G., Alan Harrison, Daniel J. Buckley, et al. "Prey field switching based on preferential behaviour can induce Lévy flights." Journal of The Royal Society Interface 10, no. 78 (2013): 20120489. https://doi.org/10.5281/zenodo.13450094.

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Abstract:

(Uploaded by Plazi for the Bat Literature Project) Using the foraging movements of an insectivorous bat, Myotis mystacinus , we describe temporal switching of foraging behaviour in response to resource availability. These observations conform to predictions of optimized search under the Lévy flight paradigm. However, we suggest that this occurs as a result of a preference behaviour and knowledge of resource distribution. Preferential behaviour and knowledge of a familiar area generate distinct movement patterns as resource availability changes on short temporal scales. The behavioural response

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42

Neuenkirch, Andreas, and Taras Shalaiko. "The maximum rate of convergence for the approximation of the fractional Lévy area at a single point." Journal of Complexity 33 (April 2016): 107–17. http://dx.doi.org/10.1016/j.jco.2015.09.008.

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43

De Bruyne, Benjamin, Satya N. Majumdar, Henri Orland, and Grégory Schehr. "Generating stochastic trajectories with global dynamical constraints." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 12 (2021): 123204. http://dx.doi.org/10.1088/1742-5468/ac3e70.

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Abstract We propose a method to exactly generate Brownian paths x c (t) that are constrained to return to the origin at some future time t f , with a given fixed area A f = ∫ 0 t f d t x c ( t ) under their trajectory. We derive an exact effective Langevin equation with an effective force that accounts for the constraint. In addition, we develop the corresponding approach for discrete-time random walks, with arbitrary jump distributions including Lévy flights, for which we obtain an effective jump distribution that encodes the constraint. Finally, we generalise our method to other types of dyn

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44

van Steijn, Leonie, Inge M. N. Wortel, Clément Sire, Loïc Dupré, Guy Theraulaz, and Roeland M. H. Merks. "Computational modelling of cell motility modes emerging from cell-matrix adhesion dynamics." PLOS Computational Biology 18, no. 2 (2022): e1009156. http://dx.doi.org/10.1371/journal.pcbi.1009156.

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Lymphocytes have been described to perform different motility patterns such as Brownian random walks, persistent random walks, and Lévy walks. Depending on the conditions, such as confinement or the distribution of target cells, either Brownian or Lévy walks lead to more efficient interaction with the targets. The diversity of these motility patterns may be explained by an adaptive response to the surrounding extracellular matrix (ECM). Indeed, depending on the ECM composition, lymphocytes either display a floating motility without attaching to the ECM, or sliding and stepping motility with re

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45

Lian, Zhigang, Dan Luo, Bingrong Dai, and Yangquan Chen. "A Lévy Distribution Based Searching Scheme for the Discrete Targets in Vast Region." Symmetry 14, no. 2 (2022): 272. http://dx.doi.org/10.3390/sym14020272.

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This paper investigates the Discrete Targets Search Problem, (DTSP), which aims to quickly search for discrete objects scattered in a vast symmetry region. Different from continuous function extremal value search, the discrete points search cannot make use of the properties of regular functions, such as function analytic, single/multiple extreme, and monotonicity. Thus, in this paper a new search scheme based on Lévy random distribution is investigated. In comparison with the TraditionalCarpet search or Random search based on other distributions, DTSP can provide much faster search speed which

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46

Freitas, C., R. Caldeira, J. Reis, and T. Dellinger. "Foraging behavior of juvenile loggerhead sea turtles in the open ocean: from Lévy exploration to area-restricted search." Marine Ecology Progress Series 595 (May 14, 2018): 203–15. http://dx.doi.org/10.3354/meps12581.

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47

Kanagasabai, Lenin. "LEVY BASED PHRYNOSOMA DOUGLASSII SWARM, ALASHAN WAPITI OPTIMIZATION, FOREST PONY ALGORITHM AND PANTHERA TIGRIS CORBETTI SEARCH FOR TRUE POWER LOSS REDUCTION IN ELECTRICAL SYSTEM." Suranaree Journal of Science and Technology 31, no. 5 (2024): 010332(1–15). https://doi.org/10.55766/sujst-2024-05-e03917.

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Lévy based Phrynosoma douglassii inspired optimization (LPD) algorithm, Alashan wapiti optimization (AWO) algorithm, Forest Pony Optimization (FPO) algorithm and Panthera Tigris corbetti optimization (PTC) algorithm are applied to solve the true power loss reduction problem. Camouflage, colour changing, blood spouting and squirt out protection methods of Phrynosoma douglassii are scientifically formulated in the LPD algorithm. Due to Camouflage action, Phrynosoma douglassii alter its body colorant by flattering luminous to evade exposure to the predators. AWO algorithm is formulated based on t

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48

Gehringer, Johann, Xue-Mei Li, and Julian Sieber. "Functional limit theorems for Volterra processes and applications to homogenization*." Nonlinearity 35, no. 4 (2022): 1521–57. http://dx.doi.org/10.1088/1361-6544/ac4818.

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Abstract We prove an enhanced limit theorem for additive functionals of a multi-dimensional Volterra process ( y t ) t ⩾ 0 in the rough path topology. As an application, we establish weak convergence as ɛ → 0 of the solution of the random ordinary differential equation (ODE) d d t x t ε = 1 ε f ( x t ε , y t ε ) and show that its limit solves a rough differential equation driven by a Gaussian field with a drift coming from the Lévy area correction of the limiting rough driver. Furthermore, we prove that the stochastic flows of the random ODE converge to those of the Kunita type Itô SDE dx t =

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Donati-Martin, C., and M. Yor. "On some examples of quadratic functionals of Brownian motion." Advances in Applied Probability 25, no. 03 (1993): 570–84. http://dx.doi.org/10.1017/s0001867800025556.

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During the last few years, several variants of P. Lévy's formula for the stochastic area of complex Brownian motion have been obtained. These are of interest in various domains of applied probability, particularly in relation to polymer studies. The method used by most authors is the diagonalization procedure of Paul Lévy. Here we derive one such variant of Lévy's formula, due to Chan, Dean, Jansons and Rogers, via a change of probability method, which reduces the computation of Laplace transforms of Brownian quadratic functionals to the computations of the means and variances of some adequate

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Diehl, Joscha, Harald Oberhauser, and Sebastian Riedel. "A Lévy area between Brownian motion and rough paths with applications to robust nonlinear filtering and rough partial differential equations." Stochastic Processes and their Applications 125, no. 1 (2015): 161–81. http://dx.doi.org/10.1016/j.spa.2014.08.005.

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