Relevant bibliographies by topics / Brownian Motion model

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Brownian Motion model'

Author: Grafiati
Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "Brownian Motion model"

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Zhu, Jubo, and Diannong Liang. "Combinatorial fractal Brownian motion model." Science in China Series E: Technological Sciences 43, no. 3 (June 2000): 254–62. http://dx.doi.org/10.1007/bf02916829.

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Areerak, Tidarut. "Mathematical Model of Stock Prices via a Fractional Brownian Motion Model with Adaptive Parameters." ISRN Applied Mathematics 2014 (April 7, 2014): 1–6. http://dx.doi.org/10.1155/2014/791418.

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The paper presents a mathematical model of stock prices using a fractional Brownian motion model with adaptive parameters (FBMAP). The accuracy index of the proposed model is compared with the Brownian motion model with adaptive parameters (BMAP). The parameters in both models are adapted at any time. The ADVANC Info Service Public Company Limited (ADVANC) and Land and Houses Public Company Limited (LH) closed prices are concerned in the paper. The Brownian motion model with adaptive parameters (BMAP) and fractional Brownian motion model with adaptive parameters (FBMAP) are applied to identify ADVANC and LH closed prices. The simulation results show that the FBMAP is more suitable for forecasting the ADVANC and LH closed price than the BMAP.
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Chang, Ying, Yiming Wang, and Sumei Zhang. "Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility." Mathematics 9, no. 2 (January 8, 2021): 126. http://dx.doi.org/10.3390/math9020126.

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Based on the present studies about the application of approximative fractional Brownian motion in the European option pricing models, our goal in the article is that we adopt the creative model by adding approximative fractional stochastic volatility to double Heston model with jumps since approximative fractional Brownian motion is more proper for application than Brownian motion in building option pricing models based on financial market data. We are the first to adopt the creative model. We derive the pricing formula for the options and the formula for the characteristic function. We also estimate the parameters with the loss function for the model and two nested models and compare the performance among those models based on the market data. The outcome illustrates that the model offers the best performance among the three models. It demonstrates that approximative fractional Brownian motion is more proper for application than Brownian motion.
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Chang, Ying, Yiming Wang, and Sumei Zhang. "Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility." Mathematics 9, no. 2 (January 8, 2021): 126. http://dx.doi.org/10.3390/math9020126.

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Based on the present studies about the application of approximative fractional Brownian motion in the European option pricing models, our goal in the article is that we adopt the creative model by adding approximative fractional stochastic volatility to double Heston model with jumps since approximative fractional Brownian motion is more proper for application than Brownian motion in building option pricing models based on financial market data. We are the first to adopt the creative model. We derive the pricing formula for the options and the formula for the characteristic function. We also estimate the parameters with the loss function for the model and two nested models and compare the performance among those models based on the market data. The outcome illustrates that the model offers the best performance among the three models. It demonstrates that approximative fractional Brownian motion is more proper for application than Brownian motion.
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KIM, JONG U. "MODEL FOR THE MOTILITY OF FLAGELLATED BACTERIA." Fluctuation and Noise Letters 08, no. 02 (June 2008): L197—L206. http://dx.doi.org/10.1142/s0219477508004386.

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Small flagellated bacteria cannot swim in a straight course due to rotational Brownian motion. By using Langevin equation and rotational diffusion equation we develop a model for the flagellated bacterial motion; thus, the model includes the rotational Brownian motion. Our model shows that the rotational Brownian motion is more significant at smaller turn angle during a tumble. It is also compared with experiment data.
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Bahamonde, Natalia, Soledad Torres, and Ciprian A. Tudor. "ARCH model and fractional Brownian motion." Statistics & Probability Letters 134 (March 2018): 70–78. http://dx.doi.org/10.1016/j.spl.2017.10.003.

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Cataldo, H. M., and E. S. Hern�ndez. "Non-Markovian quantal Brownian motion model." Journal of Statistical Physics 50, no. 1-2 (January 1988): 383–403. http://dx.doi.org/10.1007/bf01023000.

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Bocquet, L., J. P. Hansen, and J. Piasecki. "A kinetic model for Brownian motion." Il Nuovo Cimento D 16, no. 8 (August 1994): 981–91. http://dx.doi.org/10.1007/bf02458783.

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Pandey, Akhilesh. "Brownian-motion model of discrete spectra." Chaos, Solitons & Fractals 5, no. 7 (July 1995): 1275–85. http://dx.doi.org/10.1016/0960-0779(94)e0065-w.

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Manurung, Tohap. "Hubungan Antara Brownian Motion (The Winner Process) dan Surplus Process." JURNAL ILMIAH SAINS 12, no. 1 (April 30, 2012): 47. http://dx.doi.org/10.35799/jis.12.1.2012.401.

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HUBUNGAN ANTARA BROWNIAN MOTION (THE WIENER PROCESS) DAN SURPLUS PROCESS ABSTRAK Suatu analisis model continous-time menjadi cakupan yang akan dibahas dalam tulisan ini. Dengan demikian pengenalan proses stochastic akan sangat berperan. Dua proses akan di analisis yaitu proses compound Poisson dan Brownian motion. Proses compound Poisson sudah menjadi model standard untuk Ruin analysis dalam ilmu aktuaria. Sementara Brownian motion sangat berguna dalam teori keuangan modern dan juga dapat digunakan sebagai approksimasi untuk proses compound Poisson. Hal penting dalam tulisan ini adalah menujukkan bagaimana surplus process berdasarkan proses resiko compound Poisson dihubungkan dengan Brownian motion with Drift Process. Kata kunci: Brownian motion with Drift process, proses surplus, compound Poisson RELATIONSHIP BETWEEN BROWNIAN MOTION (THE WIENER PROCESS) AND THE SURPLUS PROCESS ABSTRACT An analysis of continous-time models is covered in this paper. Thus, this requires an introduction to stochastic processes. Two processes are analyzed: the compound Poisson process and Brownian motion. The compound Poisson process has been the standard model for ruin analysis in actuarial science, while Brownian motion has found considerable use in modern financial theory and also can be used as an approximation to the compound Pisson process. The important thing is to show how the surplus process based on compound poisson risk process is related to Brownian motion with drift process. Keywords: Brownian motion with drift process, surplus process, compound Poisson
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Dissertations / Theses on the topic "Brownian Motion model"

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Lampo, Aniello, Soon Hoe Lim, Jan Wehr, Pietro Massignan, and Maciej Lewenstein. "Lindblad model of quantum Brownian motion." AMER PHYSICAL SOC, 2016. http://hdl.handle.net/10150/622483.

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The theory of quantum Brownian motion describes the properties of a large class of open quantum systems. Nonetheless, its description in terms of a Born-Markov master equation, widely used in the literature, is known to violate the positivity of the density operator at very low temperatures. We study an extension of existing models, leading to an equation in the Lindblad form, which is free of this problem. We study the dynamics of the model, including the detailed properties of its stationary solution, for both constant and position-dependent coupling of the Brownian particle to the bath, focusing in particular on the correlations and the squeezing of the probability distribution induced by the environment.
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Mota, Pedro José dos Santos Palhinhas. "Brownian motion with drift threshold model." Doctoral thesis, FCT - UNL, 2008. http://hdl.handle.net/10362/1766.

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In this thesis we implement estimating procedures in order to estimate threshold parameters for the continuous time threshold models driven by stochastic di®erential equations. The ¯rst procedure is based on the EM (expectation-maximization) algorithm applied to the threshold model built from the Brownian motion with drift process. The second procedure mimics one of the fundamental ideas in the estimation of the thresholds in time series context, that is, conditional least squares estimation. We implement this procedure not only for the threshold model built from the Brownian motion with drift process but also for more generic models as the ones built from the geometric Brownian motion or the Ornstein-Uhlenbeck process. Both procedures are implemented for simu- lated data and the least squares estimation procedure is also implemented for real data of daily prices from a set of international funds. The ¯rst fund is the PF-European Sus- tainable Equities-R fund from the Pictet Funds company and the second is the Parvest Europe Dynamic Growth fund from the BNP Paribas company. The data for both funds are daily prices from the year 2004. The last fund to be considered is the Converging Europe Bond fund from the Schroder company and the data are daily prices from the year 2005.
European Community's Human Po-tential Programme under contract HPRN-CT-2000-00100, DYNSTOCH and by PRODEP III (medida 5 - Acção 5.3)
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Betz, Volker. "Gibbs measures relative to Brownian motion and Nelson's model." [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964465647.

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Endres, Derek. "Development and Demonstration of a General-Purpose Model for Brownian Motion." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1307459444.

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Mbona, Innocent. "Portfolio risk measures and option pricing under a Hybrid Brownian motion model." Diss., University of Pretoria, 2017. http://hdl.handle.net/2263/64068.

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The 2008/9 financial crisis intensified the search for realistic return models, that capture real market movements. The assumed underlying statistical distribution of financial returns plays a crucial role in the evaluation of risk measures, and pricing of financial instruments. In this dissertation, we discuss an empirical study on the evaluation of the traditional portfolio risk measures, and option pricing under the hybrid Brownian motion model, developed by Shaw and Schofield. Under this model, we derive probability density functions that have a fat-tailed property, such that “25-sigma” or worse events are more probable. We then estimate Value-at-Risk (VaR) and Expected Shortfall (ES) using four equity stocks listed on the Johannesburg Stock Exchange, including the FTSE/JSE Top 40 index. We apply the historical method and Variance-Covariance method (VC) in the valuation of VaR. Under the VC method, we adopt the GARCH(1,1) model to deal with the volatility clustering phenomenon. We backtest the VaR results and discuss our findings for each probability density function. Furthermore, we apply the hybrid model to price European style options. We compare the pricing performance of the hybrid model to the classical Black-Scholes model.
Dissertation (MSc)--University of Pretoria, 2017.
National Research Fund (NRF), University of Pretoria Postgraduate bursary and the General Studentship bursary
Mathematics and Applied Mathematics
MSc
Unrestricted
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Salopek, Donna Mary. "Tolerance to arbitrage, inclusion of fractional Brownian motion to model stock price fluctuations." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq22176.pdf.

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Salopek, Donna Mary Carleton University Dissertation Mathematics and Statistics. "Tolerance to arbitrage: inclusion of fractional Brownian motion to model stock price fluctuations." Ottawa, 1997.

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Walljee, Raabia. "The Levy-LIBOR model with default risk." Thesis, Stellenbosch : Stellenbosch University, 2015. http://hdl.handle.net/10019.1/96957.

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Thesis (MSc)--Stellenbosch University, 2015
ENGLISH ABSTRACT : In recent years, the use of Lévy processes as a modelling tool has come to be viewed more favourably than the use of the classical Brownian motion setup. The reason for this is that these processes provide more flexibility and also capture more of the ’real world’ dynamics of the model. Hence the use of Lévy processes for financial modelling is a motivating factor behind this research presentation. As a starting point a framework for the LIBOR market model with dynamics driven by a Lévy process instead of the classical Brownian motion setup is presented. When modelling LIBOR rates the use of a more realistic driving process is important since these rates are the most realistic interest rates used in the market of financial trading on a daily basis. Since the financial crisis there has been an increasing demand and need for efficient modelling and management of risk within the market. This has further led to the motivation of the use of Lévy based models for the modelling of credit risky financial instruments. The motivation stems from the basic properties of stationary and independent increments of Lévy processes. With these properties, the model is able to better account for any unexpected behaviour within the market, usually referred to as "jumps". Taking both of these factors into account, there is much motivation for the construction of a model driven by Lévy processes which is able to model credit risk and credit risky instruments. The model for LIBOR rates driven by these processes was first introduced by Eberlein and Özkan (2005) and is known as the Lévy-LIBOR model. In order to account for the credit risk in the market, the Lévy-LIBOR model with default risk was constructed. This was initially done by Kluge (2005) and then formally introduced in the paper by Eberlein et al. (2006). This thesis aims to present the theoretical construction of the model as done in the above mentioned references. The construction includes the consideration of recovery rates associated to the default event as well as a pricing formula for some popular credit derivatives.
AFRIKAANSE OPSOMMING : In onlangse jare, is die gebruik van Lévy-prosesse as ’n modellerings instrument baie meer gunstig gevind as die gebruik van die klassieke Brownse bewegingsproses opstel. Die rede hiervoor is dat hierdie prosesse meer buigsaamheid verskaf en die dinamiek van die model wat die praktyk beskryf, beter hierin vervat word. Dus is die gebruik van Lévy-prosesse vir finansiële modellering ’n motiverende faktor vir hierdie navorsingsaanbieding. As beginput word ’n raamwerk vir die LIBOR mark model met dinamika, gedryf deur ’n Lévy-proses in plaas van die klassieke Brownse bewegings opstel, aangebied. Wanneer LIBOR-koerse gemodelleer word is die gebruik van ’n meer realistiese proses belangriker aangesien hierdie koerse die mees realistiese koerse is wat in die finansiële mark op ’n daaglikse basis gebruik word. Sedert die finansiële krisis was daar ’n toenemende aanvraag en behoefte aan doeltreffende modellering en die bestaan van risiko binne die mark. Dit het verder gelei tot die motivering van Lévy-gebaseerde modelle vir die modellering van finansiële instrumente wat in die besonder aan kridietrisiko onderhewig is. Die motivering spruit uit die basiese eienskappe van stasionêre en onafhanklike inkremente van Lévy-prosesse. Met hierdie eienskappe is die model in staat om enige onverwagte gedrag (bekend as spronge) vas te vang. Deur hierdie faktore in ag te neem, is daar genoeg motivering vir die bou van ’n model gedryf deur Lévy-prosesse wat in staat is om kredietrisiko en instrumente onderhewig hieraan te modelleer. Die model vir LIBOR-koerse gedryf deur hierdie prosesse was oorspronklik bekendgestel deur Eberlein and Özkan (2005) en staan beken as die Lévy-LIBOR model. Om die kredietrisiko in die mark te akkommodeer word die Lévy-LIBOR model met "default risk" gekonstrueer. Dit was aanvanklik deur Kluge (2005) gedoen en formeel in die artikel bekendgestel deur Eberlein et al. (2006). Die doel van hierdie tesis is om die teoretiese konstruksie van die model aan te bied soos gedoen in die bogenoemde verwysings. Die konstruksie sluit ondermeer in die terugkrygingskoers wat met die wanbetaling geassosieer word, sowel as ’n prysingsformule vir ’n paar bekende krediet afgeleide instrumente.
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Froemel, Anneliese [Verfasser], and Detlef [Akademischer Betreuer] Dürr. "A semi-realistic model for Brownian motion in one dimension / Anneliese Froemel ; Betreuer: Detlef Dürr." München : Universitätsbibliothek der Ludwig-Maximilians-Universität, 2020. http://d-nb.info/1220631914/34.

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Kelekele, Liloo Didier Joel. "Mathematical model of performance measurement of defined contribution pension funds." University of the Western Cape, 2015. http://hdl.handle.net/11394/4367.

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>Magister Scientiae - MSc
The industry of pension funds has become one of the drivers of today’s economic activity by its important volume of contribution in the financial market and by creating wealth. The increasing importance that pension funds have acquired in today’s economy and financial market, raises special attention from investors, financial actors and pundits in the sector. Regarding this economic weight of pension funds, a thorough analysis of the performance of different pension funds plans in order to optimise benefits need to be undertaken. The research explores criteria and invariants that make it possible to compare the performance of different pension fund products. Pension fund companies currently do measure their performances with those of others. Likewise, the individual investing in a pension plan compares different products available in the market. There exist different ways of measuring the performance of a pension fund according to their different schemes. Generally, there exist two main pension funds plans. The defined benefit (DB) pension funds plan which is mostly preferred by pension members due to his ability to hold the risk to the pension fund manager. The defined contributions (DC) pension fund plan on the other hand, is more popularly preferred by the pension fund managers due to its ability to transfer the risk to the pension fund members. One of the reasons that motivate pension fund members’ choices of entering into a certain programme is that their expectations of maintaining their living lifestyle after retirement are met by the pension fund strategies. This dissertation investigates the various properties and characteristics of the defined contribution pension fund plan with a minimum guarantee and benchmark in order to mitigate the risk that pension fund members are subject to. For the pension fund manager the aim is to find the optimal asset allocation strategy which optimises its retribution which is in fact a part of the surplus (the difference between the pension fund value and the guarantee) (2004) [19] and to analyse the effect of sharing between the contributor and the pension fund. From the pension fund members’ perspective it is to define a optimal guarantee as a solution to the contributor’s optimisation programme. In particular, we consider a case of a pension fund company which invests in a bond, stocks and a money market account. The uncertainty in the financial market is driven by Brownian motions. Numerical simulations were performed to compare the different models.
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Books on the topic "Brownian Motion model"

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Wiersema, Ubbo F. Brownian Motion Calculus. New York: John Wiley & Sons, Ltd., 2008.

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Wiersema, Ubbo F. Brownian motion calculus. Chichester: John Wiley & Sons, 2008.

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Stochastic calculus for fractional Brownian motion and related processes. Berlin: Springer-Verlag, 2008.

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Nourdin, Ivan. Selected Aspects of Fractional Brownian Motion. Milano: Springer Milan, 2012.

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Jean, Bertoin, Martinelli F, Peres Y, Bernard P. 1944-, Bertoin Jean, Martinelli F, and Peres Y, eds. Lectures on probability theory and statistics: Ecole d'été de probabilités de Saint-Flour XXVII, 1997. Berlin: Springer, 2000.

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Ecole d'été de probabilités de Saint-Flour (27th 1997). Lectures on probability theory and statistics: Ecole d'eté de probabilités de Saint-Flour XXVII, 1997. Edited by Bertoin Jean, Martinelli F, Peres Y, and Bernard P. 1944-. Berlin: Springer, 1999.

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Quantization in astrophysics, Brownian motion and supersymmetry: Including articles never before published. Chennai, Tamil Nadu: MathTiger, 2007.

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Weilin, Xiao, ed. Fen shu Bulang yun dong xia gu ben quan zheng ding jia yan jiu: Mo xing yu can shu gu ji. Beijing: Ke xue chu ban she, 2013.

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Froot, Kenneth. Stochastic process switching: Some simple solutions. Cambridge, MA: National Bureau of Economic Research, 1989.

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E, Shreve Steven, ed. Methods of mathematical finance. New York: Springer, 1998.

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Book chapters on the topic "Brownian Motion model"

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Lin, Jennifer Shu-Jen. "Inventory Model with Fractional Brownian Motion Demand." In Computational Collective Intelligence. Technologies and Applications, 252–59. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16693-8_27.

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Petters, Arlie O., and Xiaoying Dong. "Stochastic Calculus and Geometric Brownian Motion Model." In An Introduction to Mathematical Finance with Applications, 253–327. New York, NY: Springer New York, 2016. http://dx.doi.org/10.1007/978-1-4939-3783-7_6.

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Lampo, Aniello, Miguel Ángel García March, and Maciej Lewenstein. "A Lindblad Model for Quantum Brownian Motion." In SpringerBriefs in Physics, 57–72. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16804-9_5.

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Azizi, Seyed Mohammad Esmaeil Pour Mohamma, and Abdolsadeh Neisy. "A New Approach in Geometric Brownian Motion Model." In Advances in Intelligent Systems and Computing, 336–42. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-66514-6_34.

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Holley, Richard. "The One Dimensional Stochastic X-Y Model." In Random Walks, Brownian Motion, and Interacting Particle Systems, 295–307. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0459-6_16.

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Al-Kadi, Omar S., Allen Lu, Albert J. Sinusas, and James S. Duncan. "Stochastic Model-Based Left Ventricle Segmentation in 3D Echocardiography Using Fractional Brownian Motion." In Statistical Atlases and Computational Models of the Heart. Atrial Segmentation and LV Quantification Challenges, 77–84. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-12029-0_9.

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Shiryaev, Albert N. "Multi-stage Quickest Detection of Breakdown of a Stationary Regime. Model with Brownian Motion." In Stochastic Disorder Problems, 217–37. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-01526-8_7.

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Ord, G. N. "Obtaining the Schrödinger and Dirac Equations from the Einstein/KAC Model of Brownian Motion by Projection." In The Present Status of the Quantum Theory of Light, 169–80. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-011-5682-0_18.

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Tucker, Susan C. "Reaction rates in condensed phases. Perspective on “Brownian motion in a field of force and the diffusion model of chemical reactions”." In Theoretical Chemistry Accounts, 209–11. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-10421-7_12.

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Felderhof, B. U., and R. B. Jones. "Orientational Relaxation and Brownian Motion." In Dynamics: Models and Kinetic Methods for Non-equilibrium Many Body Systems, 31–38. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-011-4365-3_3.

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Conference papers on the topic "Brownian Motion model"

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Ioannidis, S., and P. Marbach. "A Brownian Motion Model for Last Encounter Routing." In Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications. IEEE, 2006. http://dx.doi.org/10.1109/infocom.2006.301.

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Ching, Soo Huei, and Pooi Ah Hin. "Brownian motion model with stochastic parameters for asset prices." In INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS 2013 (ICMSS2013): Proceedings of the International Conference on Mathematical Sciences and Statistics 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4823962.

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MÖLLER, P., and J. RANDRUP. "FISSION-FRAGMENT CHARGE YIELDS IN A BROWNIAN SHAPE-MOTION MODEL." In Proceedings of the Fifth International Conference on ICFN5. WORLD SCIENTIFIC, 2013. http://dx.doi.org/10.1142/9789814525435_0075.

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Zhao, Wei. "Research on Fractional Option Pricing Model Under Real Brownian Motion Environment." In 2009 First International Conference on Information Science and Engineering. IEEE, 2009. http://dx.doi.org/10.1109/icise.2009.954.

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Jiang, Aiping, Xiangxue Zhang, Luping Jiang, and Jingquan Wang. "A Wavelet Domain Watermarking Algorithm Based on Fractional Brownian Motion Model." In 2012 5th International Workshop on Chaos-Fractals Theories and Applications (IWCFTA). IEEE, 2012. http://dx.doi.org/10.1109/iwcfta.2012.68.

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Su, Gang, Yingzhuang Liu, and Hao Chen. "An adaptive channel prediction algorithm based on fractal Brownian motion model." In International Conference on Space information Technology, edited by Cheng Wang, Shan Zhong, and Xiulin Hu. SPIE, 2005. http://dx.doi.org/10.1117/12.657301.

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Prasher, Ravi. "Brownian-Motion-Based Convective-Conductive Model for the Thermal Conductivity of Nanofluids." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72048.

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The research community has been perplexed for the past five years with the unusually high effective thermal conductivity of nanofluids. Although various mechanisms and models have been proposed in the literature to explain the high conductivity of these nanofluids, no concrete conclusions have been reached. Through an order-of-magnitude analysis of various possible mechanisms, we show that convection caused by the Brownian movement of these nanoparticles is primarily responsible for the enhancement in the thermal conductivity of such colloidal nanofluids. We also introduce a convective-conductive model which accurately captures the effects of particle size, choice of base liquid, thermal interfacial resistance between the particles and liquid, temperature, etc. This model is a combination of the Maxwell-Garnett (MG) conduction model and the convection caused by the Brownian movement of the nanoparticles, and reduces to the MG model for large particle sizes.
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Zhang Qimin and Li Xining. "Asymptotic stability of stochastic delay Lotka-Volterra model with fractional Brownian motion." In 2010 8th World Congress on Intelligent Control and Automation (WCICA 2010). IEEE, 2010. http://dx.doi.org/10.1109/wcica.2010.5554981.

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Aitken, George J. M., Delphine Rossille, and Donald R. McGaughey. "Filtered fractional Brownian motion as a model for atmospherically induced wavefront distortions." In Optical Science, Engineering and Instrumentation '97, edited by Luc R. Bissonnette and Christopher Dainty. SPIE, 1997. http://dx.doi.org/10.1117/12.279028.

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10

Zachevsky, Ido, and Yehoshua Y. Zeevi. "Denoising of natural stochastic colored-textures based on fractional brownian motion model." In 2015 IEEE International Conference on Image Processing (ICIP). IEEE, 2015. http://dx.doi.org/10.1109/icip.2015.7350963.

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