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040 _aOCoLC-P
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020 _a9781000338799
_q(ePub ebook)
020 _a1000338797
020 _a9781000338775
_q(PDF ebook)
020 _a1000338770
020 _a9781003098133
_q(ebook)
020 _a1003098134
020 _a9781000338782
_q(electronic bk. : Mobipocket)
020 _a1000338789
_q(electronic bk. : Mobipocket)
020 _z9780367564940 (hbk.)
024 7 _a10.1201/9781003098133
_2doi
035 _a(OCoLC)1233301924
035 _a(OCoLC-P)1233301924
050 4 _aQA274.73
072 7 _aMAT
_x029040
_2bisacsh
072 7 _aSCI
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072 7 _aMAT
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072 7 _aPBWL
_2bicssc
082 0 4 _a519.233
_223
100 1 _aKolesnik, Alexander D.,
_eauthor.
245 1 0 _aMarkov random flights /
_cAlexander D. Kolesnik.
250 _a1st.
264 1 _aBoca Raton :
_bChapman & Hall/CRC,
_c2021.
300 _a1 online resource :
_billustrations (black and white).
336 _atext
_2rdacontent
336 _astill image
_2rdacontent
337 _acomputer
_2rdamedia
338 _aonline resource
_2rdacarrier
490 0 _aChapman & Hall/CRC monographs and research notes in mathematics
500 _a<P><STRONG>1. Preliminaries.</STRONG> 1.1. Markov processes. 1.2. Random evolutions. 1.3. Determinant theorem. 1.4. Kurtz's diffusion approximation theorem. 1.5. Special functions. 1.6. Hypergeometric functions. 1.7. Generalized functions. 1.8. Integral transforms. 1.9. Auxiliary lemmas. <STRONG>2. Telegraph Processes.</STRONG> 2.1. Definition of the process and structure of distribution. 2.2. Kolmogorov equation. 2.3. Telegraph equation. 2.4. Characteristic function. 2.5. Transition density. 2.6. Probability distribution function. 2.7. Convergence to the Wiener process. 2.8. Laplace transform of transition density. 2.9. Moment analysis. 2.11. Telegraph-type processes with several velocities. 2.12. Euclidean distance between two telegraph processes. 2.13. Sum of two telegraph processes. 2.14. Linear combinations of telegraph processes. <B>3. Planar Random Motion with a Finite Number of Directions. </B>3.1. Description of the model and the main result. 3.2. Proof of the Main Theorem. 3.3. Diffusion area. 3.4. Polynomial representations of the generator. 3.5. Limiting differential operator. 3.6. Weak convergence to the Wiener process. <B>4. Integral Transforms of the Distributions of Markov Random Flights. </B>4.1. Description of process and structure of distribution. 4.2. Recurrent integral relations. 4.3. Laplace transforms of conditional characteristic functions. 4.4. Conditional characteristic functions. 4.5. Integral equation for characteristic function. 4.6. Laplace transform of characteristic function. 4.7. Initial conditions. 4.8. Limit theorem. 4.9. Random flight with rare switching. 4.10. Hyper-parabolic operators. 4.11. Random flight with arbitrary dissipation function. 4.12. Integral equation for transition density. <B>5. Markov Random Flight in the Plane </B>R<SUB>2</SUB>. 5.1. Conditional densities. 5.2 Distribution of the process. 5.3. Characteristic function. 5.4 Telegraph equation. 5.5. Limit theorem. 5.6. Alternative derivation of transition density. 5.7. Moments. 5.8. Random flight with Gaussian starting point. 5.9. Euclidean distance between two random flights. <B>6. Markov Random Flight in the Space </B>R<SUB>3</SUB>. 6.1. Characteristic function. 6.2. Discontinuous term of distribution. 6.3. Limit theorem. 6.4. Asymptotic relation for the transition density. 6.5. Fundamental solution to Kolmogorov equation. <B>7. Markov Random Flight in the Space </B>R<SUB>4. </SUB><B></B>7.1. Conditional densities. 7.2. Distribution of the process. 7.3. Characteristic function. 7.4. Limit theorem. 7.5. Moments. <B>8. Markov Random Flight in the Space </B>R<SUB>6</SUB>. 8.1. Conditional densities. 8.2. Distribution of the process. <B>9. Applied Models. </B>9.1. Slow diffusion. 9.2. Fluctuations of water level in reservoir. 9.3. Pollution model. 9.4. Physical applications. 9.5 Option pricing. </P>
520 _aMarkov Random Flights is the first systematic presentation of the theory of Markov random flights in the Euclidean spaces of different dimensions. Markov random flights is a stochastic dynamic system subject to the control of an external Poisson process and represented by the stochastic motion of a particle that moves at constant finite speed and changes its direction at random Poisson time instants. The initial (and each new) direction is taken at random according to some probability distribution on the unit sphere. Such stochastic motion is the basic model for describing many real finite-velocity transport phenomena arising in statistical physics, chemistry, biology, environmental science and financial markets. Markov random flights acts as an effective tool for modelling the slow and super-slow diffusion processes arising in various fields of science and technology. Features: Provides the first systematic presentation of the theory of Markov random flights in the Euclidean spaces of different dimensions. Suitable for graduate students and specialists and professionals in applied areas. Introduces a new unified approach based on the powerful methods of mathematical analysis, such as integral transforms, generalized, hypergeometric and special functions. Author Alexander D. Kolesnik is a professor, Head of Laboratory (2015-2019) and principal researcher (since 2020) at the Institute of Mathematics and Computer Science, Kishinev (Chiinu), Moldova. He graduated from Moldova State University in 1980 and earned his PhD from the Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev in 1991. He also earned a PhD Habilitation in mathematics and physics with specialization in stochastic processes, probability and statistics conferred by the Specialized Council at the Institute of Mathematics of the National Academy of Sciences of Ukraine and confirmed by the Supreme Attestation Commission of Ukraine in 2010. His research interests include: probability and statistics, stochastic processes, random evolutions, stochastic dynamic systems, random flights, diffusion processes, transport processes, random walks, stochastic processes in random environments, partial differential equations in stochastic models, statistical physics and wave processes. Dr. Kolesnik has published more than 70 scientific publications, mostly in high-standard international journals and a monograph. He has also acted as external referee for many outstanding international journals in mathematics and physics, being awarded by the "Certificate of Outstanding Contribution in Reviewing" from the journal "Stochastic Processes and their Applications." He was the visiting professor and scholarship holder at universities in Italy and Germany and member of the Board of Global Advisors of the International Federation of Nonlinear Analysts (IFNA), United States of America.
588 _aOCLC-licensed vendor bibliographic record.
650 0 _aRandom walks (Mathematics)
650 0 _aMarkov processes.
650 7 _aSCIENCE / Mathematical Physics
_2bisacsh
650 7 _aMATHEMATICS / Transformations
_2bisacsh
856 4 0 _3Read Online
_uhttps://www.taylorfrancis.com/books/9781003098133
856 4 2 _3OCLC metadata license agreement
_uhttp://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
942 _2lcc
_cEBK
999 _c17828
_d17828