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Добірка наукової літератури з теми "Brownian motion processes"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 30 липня 2024

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Статті в журналах з теми "Brownian motion processes"

1

Suryawan, Herry P., and José L. da Silva. "Green Measures for a Class of Non-Markov Processes." Mathematics 12, no. 9 (April 27, 2024): 1334. http://dx.doi.org/10.3390/math12091334.

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In this paper, we investigate the Green measure for a class of non-Gaussian processes in Rd. These measures are associated with the family of generalized grey Brownian motions Bβ,α, 0<β≤1, 0<α≤2. This family includes both fractional Brownian motion, Brownian motion, and other non-Gaussian processes. We show that the perpetual integral exists with probability 1 for dα>2 and 1<α≤2. The Green measure then generalizes those measures of all these classes.

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2

Takenaka, Shigeo. "Integral-geometric construction of self-similar stable processes." Nagoya Mathematical Journal 123 (September 1991): 1–12. http://dx.doi.org/10.1017/s0027763000003627.

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Recently, fractional Brownian motions are widely used to describe complex phenomena in several fields of natural science. In the terminology of probability theory the fractional Brownian motion is a Gaussian process {X(t) : t є R} with stationary increments which has a self-similar property, that is, there exists a constant H (for the Brownian motion H = 1/2, in general 0 < H < 1 for Gaussian processes) called the exponent of self-similarity of the process, such that, for any c > 0, two processes are subject to the same law (see [10]).

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3

Rosen, Jay, and Jean-Dominique Deuschel. "motion, super-Brownian motion and related processes." Annals of Probability 26, no. 2 (April 1998): 602–43. http://dx.doi.org/10.1214/aop/1022855645.

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4

Rao, Nan, Qidi Peng, and Ran Zhao. "Cluster Analysis on Locally Asymptotically Self-Similar Processes with Known Number of Clusters." Fractal and Fractional 6, no. 4 (April 14, 2022): 222. http://dx.doi.org/10.3390/fractalfract6040222.

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We conduct cluster analysis of a class of locally asymptotically self-similar stochastic processes with finite covariance structures, which includes Brownian motion, fractional Brownian motion, and multifractional Brownian motion as paradigmatic examples. Given the true number of clusters, a new covariance-based dissimilarity measure is introduced, based on which we obtain approximately asymptotically consistent algorithms for clustering locally asymptotically self-similar stochastic processes. In the simulation study, clustering data sampled from fractional and multifractional Brownian motions with distinct Hurst parameters illustrates the approximated asymptotic consistency of the proposed algorithms. Clustering global financial markets’ equity indexes returns and sovereign CDS spreads provides a successful real world application. Implementations in MATLAB of the proposed algorithms and the simulation study are publicly shared in GitHub.

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5

SOTTINEN, TOMMI, and LAURI VIITASAARI. "CONDITIONAL-MEAN HEDGING UNDER TRANSACTION COSTS IN GAUSSIAN MODELS." International Journal of Theoretical and Applied Finance 21, no. 02 (March 2018): 1850015. http://dx.doi.org/10.1142/s0219024918500152.

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We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an application, we consider conditional-mean hedging under transaction costs in Black–Scholes type pricing models where the Brownian motion is replaced with a more general regular invertible Gaussian Volterra process.

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6

Andres, Sebastian, and Lisa Hartung. "Diffusion processes on branching Brownian motion." Latin American Journal of Probability and Mathematical Statistics 15, no. 2 (2018): 1377. http://dx.doi.org/10.30757/alea.v15-51.

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7

Ouknine, Y. "“Skew-Brownian Motion” and Derived Processes." Theory of Probability & Its Applications 35, no. 1 (January 1991): 163–69. http://dx.doi.org/10.1137/1135018.

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8

Katori, Makoto, and Hideki Tanemura. "Noncolliding Brownian Motion and Determinantal Processes." Journal of Statistical Physics 129, no. 5-6 (October 13, 2007): 1233–77. http://dx.doi.org/10.1007/s10955-007-9421-y.

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9

Jedidi, Wissem, and Stavros Vakeroudis. "Windings of planar processes, exponential functionals and Asian options." Advances in Applied Probability 50, no. 3 (September 2018): 726–42. http://dx.doi.org/10.1017/apr.2018.33.

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Abstract Motivated by a common mathematical finance topic, we discuss the reciprocal of the exit time from a cone of planar Brownian motion which also corresponds to the exponential functional of Brownian motion in the framework of planar Brownian motion. We prove a conjecture of Vakeroudis and Yor (2012) concerning infinite divisibility properties of this random variable and present a novel simple proof of the result of DeBlassie (1987), (1988) concerning the asymptotic behavior of the distribution of the Bessel clock appearing in the skew-product representation of planar Brownian motion, as t→∞. We use the results of the windings approach in order to obtain results for quantities associated to the pricing of Asian options.

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10

Adler, Robert J., and Ron Pyke. "Scanning Brownian Processes." Advances in Applied Probability 29, no. 2 (June 1997): 295–326. http://dx.doi.org/10.2307/1428004.

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The ‘scanning process' Z(t), t ∈ ℝk of the title is a Gaussian random field obtained by associating with Z(t) the value of a set-indexed Brownian motion on the translate t + A0 of some ‘scanning set' A0. We study the basic properties of the random field Z relating, for example, its continuity and other sample path properties to the geometrical properties of A0. We ask if the set A0 determines the scanning process, and investigate when, and how, it is possible to recover the structure of A0 from realisations of the sample paths of the random field Z.

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Дисертації з теми "Brownian motion processes"

1

Dunkel, Jörn. "Relativistic Brownian motion and diffusion processes." kostenfrei, 2008. http://d-nb.info/991318757/34.

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2

Trefán, György. "Deterministic Brownian Motion." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc279262/.

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Анотація:

The goal of this thesis is to contribute to the ambitious program of the foundation of developing statistical physics using chaos. We build a deterministic model of Brownian motion and provide a microscpoic derivation of the Fokker-Planck equation. Since the Brownian motion of a particle is the result of the competing processes of diffusion and dissipation, we create a model where both diffusion and dissipation originate from the same deterministic mechanism - the deterministic interaction of that particle with its environment. We show that standard diffusion which is the basis of the Fokker-Planck equation rests on the Central Limit Theorem, and, consequently, on the possibility of deriving it from a deterministic process with a quickly decaying correlation function. The sensitive dependence on initial conditions, one of the defining properties of chaos insures this rapid decay. We carefully address the problem of deriving dissipation from the interaction of a particle with a fully deterministic nonlinear bath, that we term the booster. We show that the solution of this problem essentially rests on the linear response of a booster to an external perturbation. This raises a long-standing problem concerned with Kubo's Linear Response Theory and the strong criticism against it by van Kampen. Kubo's theory is based on a perturbation treatment of the Liouville equation, which, in turn, is expected to be totally equivalent to a first-order perturbation treatment of single trajectories. Since the boosters are chaotic, and chaos is essential to generate diffusion, the single trajectories are highly unstable and do not respond linearly to weak external perturbation. We adopt chaotic maps as boosters of a Brownian particle, and therefore address the problem of the response of a chaotic booster to an external perturbation. We notice that a fully chaotic map is characterized by an invariant measure which is a continuous function of the control parameters of the map. Consequently if the external perturbation is made to act on a control parameter of the map, we show that the booster distribution undergoes slight modifications as an effect of the weak external perturbation, thereby leading to a linear response of the mean value of the perturbed variable of the booster. This approach to linear response completely bypasses the criticism of van Kampen. The joint use of these two phenomena, diffusion and friction stemming from the interaction of the Brownian particle with the same booster, makes the microscopic derivation of a Fokker-Planck equation and Brownian motion, possible.

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3

Keprta, S. "Integral tests for Brownian motion and some related processes." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ26856.pdf.

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4

Keprta, Stanislav Carleton University Dissertation Mathematics and Statistics. "Integral tests for Brownian motion and some related processes." Ottawa, 1997.

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5

Cakir, Rasit Grigolini Paolo. "Fractional Brownian motion and dynamic approach to complexity." [Denton, Tex.] : University of North Texas, 2007. http://digital.library.unt.edu/permalink/meta-dc-3992.

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6

Simon, Matthieu. "Markov-modulated processes: Brownian motions, option pricing and epidemics." Doctoral thesis, Universite Libre de Bruxelles, 2017. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/250010.

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Анотація:

This thesis is devoted to the study of different stochastic processes which have a common feature: they are Markov-modulated, which means that their evolution rules depend on the state occupied by an underlying Markov process. In the first part of this thesis, we analyse the stationary distribution and various first passage problems for Markov-modulated Brownian motions (MMBMs) as well as for two extensions: MMBMs with jumps and MMBMs modified by a temporary change of regime upon visits to level zero. The second part of this thesis is devoted to the use of Markov-modulated processes in mathematical finance, more precisely for the calculation of different option prices. We use a Fourier transform approach to price different European options (vanilla, exchange and quanto options) in the case where the value of the considered risky assets evolves like the exponential of a Markov-modulated Lévy process. The third part of this thesis is devoted to the study of some stochastic epidemic processes, namely the SIR processes. In our models, a Markov process is used to modulate the behaviour of the individuals who bring the disease. We use different martingale approaches as well as matrix analytic methods to obtain various information about the state of the population when the epidemic is over.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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7

莊競誠 and King-sing Chong. "Explorations in Markov processes." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31235682.

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8

Chong, King-sing. "Explorations in Markov processes /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18736105.

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9

Duncan, Thomas. "Brownian Motion: A Study of Its Theory and Applications." Thesis, Boston College, 2007. http://hdl.handle.net/2345/505.

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Thesis advisor: Nancy Rallis
The theory of Brownian motion is an integral part of statistics and probability, and it also has some of the most diverse applications found in any topic in mathematics. With extensions into fields as vast and different as economics, physics, and management science, Brownian motion has become one of the most studied mathematical phenomena of the late twentieth and early twenty-first centuries. Today, Brownian motion is mostly understood as a type of mathematical process called a stochastic process. The word "stochastic" actually stems from the Greek word for "I guess," implying that stochastic processes tend to produce uncertain results, and Brownian motion is no exception to this, though with the right models, probabilities can be assigned to certain outcomes and we can begin to understand these complicated processes. This work reaches to attain this goal with regard to Brownian motion, and in addition it explores several applications found in the aforementioned fields and beyond
Thesis (BA) — Boston College, 2007
Submitted to: Boston College. College of Arts and Sciences
Discipline: Mathematics
Discipline: College Honors Program

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10

Hult, Henrik. "Topics on fractional Brownian motion and regular variation for stochastic processes." Doctoral thesis, KTH, Mathematics, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3604.

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The first part of this thesis studies tail probabilities forelliptical distributions and probabilities of extreme eventsfor multivariate stochastic processes. It is assumed that thetails of the probability distributions satisfy a regularvariation condition. This means, roughly speaking, that thereis a non-negligible probability for very large or extremeoutcomes to occur. Such models are useful in applicationsincluding insurance, finance and telecommunications networks.It is shown how regular variation of the marginals, or theincrements, of a stochastic process implies regular variationof functionals of the process. Moreover, the associated tailbehavior in terms of a limit measure is derived.

The second part of the thesis studies problems related toparameter estimation in stochastic models with long memory.Emphasis is on the estimation of the drift parameter in somestochastic differential equations driven by the fractionalBrownian motion or more generally Volterra-type processes.Observing the process continuously, the maximum likelihoodestimator is derived using a Girsanov transformation. In thecase of discrete observations the study is carried out for theparticular case of the fractional Ornstein-Uhlenbeck process.For this model Whittles approach is applied to derive anestimator for all unknown parameters.

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Книги з теми "Brownian motion processes"

1

1972-, Dolgopyat Dmitry, ed. Brownian Brownian motion-I. Providence, R.I: American Mathematical Society, 2009.

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2

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

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3

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

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4

Schilling, René L. Brownian motion: An introduction to stochastic processes. Berlin: De Gruyter, 2012.

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5

Lindstrøm, Tom. Brownian motion on nested fractals. Providence, R.I., USA: American Mathematical Society, 1990.

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6

Earnshaw, Robert C., and Elizabeth M. Riley. Brownian motion: Theory, modelling and applications. Hauppauge, N.Y: Nova Science Publishers, 2011.

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7

Bass, Richard F. Cutting Brownian paths. Providence, R.I: American Mathematical Society, 1999.

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8

Karatzas, Ioannis. Brownian motion and stochastic calculus. 2nd ed. New York: Springer, 1996.

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9

E, Shreve Steven, ed. Brownian motion and stochastic calculus. New York: Springer-Verlag, 1988.

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10

E, Shreve Steven, ed. Brownian motion and stochastic calculus. 2nd ed. New York: Springer-Verlag, 1991.

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Частини книг з теми "Brownian motion processes"

1

Rozanov, Yuriĭ A. "Brownian Motion." In Introduction to Random Processes, 33–43. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-72717-7_5.

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2

Resnick, Sidney I. "Brownian Motion." In Adventures in Stochastic Processes, 482–557. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0387-2_6.

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3

Korosteleva, Olga. "Brownian Motion." In Stochastic Processes with R, 153–82. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003244288-9.

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4

Koralov, Leonid, and Yakov G. Sinai. "Brownian Motion." In Theory of Probability and Random Processes, 253–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-540-68829-7_18.

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5

Hainaut, Donatien. "Fractional Brownian Motion." In Continuous Time Processes for Finance, 143–78. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-06361-9_6.

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6

Madhira, Sivaprasad, and Shailaja Deshmukh. "Brownian Motion Process." In Introduction to Stochastic Processes Using R, 487–545. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-5601-2_9.

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7

Itô, Kiyosi, and Henry P. McKean. "The standard Brownian motion." In Diffusion Processes and their Sample Paths, 5–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-62025-6_2.

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8

Bas, Esra. "Introduction to Brownian Motion." In Basics of Probability and Stochastic Processes, 253–63. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-32323-3_16.

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9

Bosq, Denis, and Hung T. Nguyen. "Brownian Motion and Diffusion Processes." In A Course in Stochastic Processes, 233–53. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8769-3_12.

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10

Kallenberg, Olav. "Gaussian Processes and Brownian Motion." In Probability and Its Applications, 249–69. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-4015-8_13.

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Тези доповідей конференцій з теми "Brownian motion processes"

1

Bilokon, Paul, and Abbas Edalat. "A domain-theoretic approach to Brownian motion and general continuous stochastic processes." In CSL-LICS '14: JOINT MEETING OF the Twenty-Third EACSL Annual Conference on COMPUTER SCIENCE LOGIC. New York, NY, USA: ACM, 2014. http://dx.doi.org/10.1145/2603088.2603102.

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2

Borhani, Alireza, and Matthias Patzold. "Modelling of non-stationary mobile radio channels using two-dimensional brownian motion processes." In 2013 International Conference on Advanced Technologies for Communications (ATC 2013). IEEE, 2013. http://dx.doi.org/10.1109/atc.2013.6698114.

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3

Cezayirli, Ahmet. "Simulation of online relative concentration measurements in chemical processes using Brownian motion and image processing." In 2020 4th International Symposium on Multidisciplinary Studies and Innovative Technologies (ISMSIT). IEEE, 2020. http://dx.doi.org/10.1109/ismsit50672.2020.9254637.

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4

Busnaina, Ahmed, Xiaoying Zhu, and Xiaowei Zheng. "Particle Transport in CVD and Diffusion Processes." In ASME 1992 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/cie1992-0057.

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Abstract Particle transport and deposition in a CVD chamber and a horizontal diffusion furnace are studied. Mean flow and thermal fields are simulated using GENFLOW, which is a general computer code for fluid flow and heat transfer computations. Trajectories of aerosol particles in the chamber and the furnace are evaluated by solving the corresponding Lagrangian equation of motion that includes effects of temperature, drag, gravity, Brownian motion and turbulence fluctuations generated during pumping or venting. Aerosol particles are released at the gas inlet and are carried towards the wafers with sizes of 0.05–1.0 micron in the CVD chamber and 1.0 micron in the diffusion furnace. Depositions of particles on the wafer, wafer temperature and inlet turbulence intensity are evaluated.

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5

Perez Rey, Luis A., Vlado Menkovski, and Jim Portegies. "Diffusion Variational Autoencoders." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/375.

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A standard Variational Autoencoder, with a Euclidean latent space, is structurally incapable of capturing topological properties of certain datasets. To remove topological obstructions, we introduce Diffusion Variational Autoencoders (DeltaVAE) with arbitrary (closed) manifolds as a latent space. A Diffusion Variational Autoencoder uses transition kernels of Brownian motion on the manifold. In particular, it uses properties of the Brownian motion to implement the reparametrization trick and fast approximations to the KL divergence. We show that the DeltaVAE is indeed capable of capturing topological properties for datasets with a known underlying latent structure derived from generative processes such as rotations and translations.

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6

Tian, L., G. Ahmadi, and J. Y. Tu. "Multi-Scale Transport Modeling: Asbestos and Nano Fibers in Inhalation Risk Assessments." In ASME 2017 Fluids Engineering Division Summer Meeting. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/fedsm2017-69083.

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Recent rapid development of the carbon nanotubes (CNTs) industry has raised health concerns as these engineered particles have the appearance of asbestos, which is a well-known inhalation hazard. Compared to asbestos, CNTs have similar elongated rod shaped structure, while they are in nano-scale where the particle motion is markedly affected by Brownian diffusion. However, limited studies on Brownian dynamics of CNTs are available in the literature and the details of motions of these elongate ultrafine particles, and in particular, their transport and deposition processes are largely unknown. In this study, multi-scale analysis of transport and deposition of elongated particles in micro and nano-scales were performed. Particular attention was given to the differences and similarities of the physical mechanisms governing the particle/fiber motions at different length scales. The study was focused on revealing the details of the interaction between elongated particles at different scales and the fluid motions. Such information is very useful in understanding the transport processes of asbestos and nano-fibers in human airways for inhalation risk assessment studies.

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7

Zare, Azam, Omid Abouali, and Goodarz Ahmadi. "A Numerical Model for Brownian Motions of Nano-Particles in Supersonic and Hypersonic Impactors." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98308.

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In this paper, transport and deposition processes of nano-particles in supersonic and hypersonic impactors were investigated using a computational modeling approach. Axisymmetric forms of the compressible Navier-Stokes and energy equations were solved and the airflow and thermal condition in the impactor including the upstream nozzle were evaluated. A computer simulation model for solving the Lagrangian particle equation of motion including all the relevant forces was developed. The importance of the accurate modeling of the Brownian motion of nano-particles was further emphasized. The motion of nano- and micro-particles in the supersonic and hypersonic impactors were then simulated and the impactor capture efficiencies under various operating conditions were studied. For dilute particle concentrations, the assumption of one-way interaction was used. Particular attention was given to proper evaluation of the Brownian motion of the nano-particles in the upstream nozzle and in the body of impactor. The simulation results for collection efficiency were found to be in good agreement with experimental data. In particular, the model accurately predicted the loss of the nano-particles in the upstream nozzle due to their Brownian motion.

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8

MacGibbon, Bruce S., and Ahmed A. Busnaina. "Mass Transport and Particle Transport in an LPCVD Process." In ASME 1993 International Computers in Engineering Conference and Exposition. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/cie1993-0027.

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Abstract Low pressure chemical vapor deposition (LPCVD) processes are used in the microelectronic manufacturing industry. As circuit dimensions decrease, it becomes ever more critical to control the particulate contamination of the wafer during fabrication. To accurately predict the particle motion, and thus minimize contamination, the flow field must be known. This paper outlines the procedure to numerically simulate the velocity, temperature, and concentration fields in a low pressure application. From these solutions, accurate particle trajectories are predicted using a Lagrangian formulation that includes effects of temperature, drag, gravity, and Brownian motion.

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9

Perez, Dario G., and Luciano Zunino. "Inner- and outer-scales of turbulent wavefront phase defined through the lens of multi-scale Levy fractional Brownian motion processes." In SPIE Remote Sensing, edited by Anton Kohnle, Karin Stein, and John D. Gonglewski. SPIE, 2008. http://dx.doi.org/10.1117/12.800155.

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10

Takana, Hidemasa, Kazuhiro Ogawa, Tetsuo Shoji, and Hideya Nishiyama. "Optimization of Cold Gas Dynamic Spray Processes by Computational Simulation." In ASME/JSME 2007 5th Joint Fluids Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/fedsm2007-37081.

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Анотація:

An integrated model of compressible thermofluid, splat formation and coating formation for a cold dynamic spray process has been established. In-flight behavior of nano-micro particles and the interaction between the shock wave and the particles in a supersonic jet flow impinging onto the substrate and further particle acceleration with electrostatic force are clarified in detail by considering viscous drag force, flow acceleration, added mass, gravity, Basset history force, Saffman lift force, Brownian motion, thermophoresis and electrostatic force. The effect of electrostatic acceleration becomes more significant with the decrease in particle diameter even in the presence of unavoidable shock wave. As a result, electrostatic acceleration can broaden the application range of operating particle diameter in a cold gas dynamic spray process to form a robust and activated coating. Finally, based on the integrated model, the coating thickness characteristics in an electrostatic assisted cold dynamic spray process are evaluated.

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Звіти організацій з теми "Brownian motion processes"

1

Adler, Robert J., and Gennady Samorodnitsky. Super Fractional Brownian Motion, Fractional Super Brownian Motion and Related Self-Similar (Super) Processes. Fort Belvoir, VA: Defense Technical Information Center, January 1991. http://dx.doi.org/10.21236/ada274696.

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2

Adler, Robert J., and Gennady Samorodnitsky. Super Fractional Brownian Motion, Fractional Super Brownian Motion and Related Self-Similar (Super) Processes. Fort Belvoir, VA: Defense Technical Information Center, January 1994. http://dx.doi.org/10.21236/ada275124.

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3

Соловйов, В. М., В. В. Соловйова та Д. М. Чабаненко. Динаміка параметрів α-стійкого процесу Леві для розподілів прибутковостей фінансових часових рядів. ФО-П Ткачук О. В., 2014. http://dx.doi.org/10.31812/0564/1336.

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Modem market economy of any country cannot successfully behave without the existence of the effective financial market. In the conditions of growing financial market, it is necessary to use modern risk-management methods, which take non-gaussian distributions into consideration. It is known, that financial and economic time series return’s distributions demonstrate so-called «heavy tails», which interrupts the modeling o f these processes with classical statistical methods. One o f the models, that is able to describe processes with «heavy tails», are the а -stable Levi processes. They can slightly simulate the dynamics of the asset prices, because it consists o f two components: the Brownian motion component and jump component. In the current work the usage of model parameters estimation procedure is proposed, which is based on the characteristic functions and is applied for the moving window for the purpose of financial-economic system’ s state monitoring.

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