MARC Record from marc_columbia

LEADER: 05455fam a2200397 a 4500
001 1443484
005 20220602035531.0
008 930903t19941994nyua b 001 0 eng
010 $a 93021359
020 $a0824788826 (acid-free paper)
035 $9AHW2913CU
035 $a(NNC)1443484
035 $a1443484
040 $aDLC$cDLC$dDLC$dNNC
050 00 $aQA274$b.J35 1994
082 00 $a003/.76$220
100 1 $aJanicki, Aleksander,$d1946-$0http://id.loc.gov/authorities/names/n93086936
245 10 $aSimulation and chaotic behavior of α-stable stochastic processes /$cAleksander Janicki, Aleksander Weron.
260 $aNew York :$bM. Dekker,$c[1994], ©1994.
300 $avii, 355 pages :$billustrations ;$c24 cm.
336 $atext$2rdacontent
337 $aunmediated$2rdamedia
338 $avolume$2rdacarrier
490 1 $aMonographs and textbooks in pure and applied mathematics ;$v178
504 $aIncludes bibliographical references (p. 339-352) and index.
505 0 $a1. Preliminary Remarks. 1.1. Historical Overview. 1.2. Stochastic [alpha]-Stable Modeling. 1.3. Statistical versus Stochastic Modeling. 1.4. Hierarchy of Chaos. 1.5. Computer Simulations and Visualizations. 1.6. Stochastic Processes -- 2. Brownian Motion, Poisson Process, [alpha]-Stable Levy Motion. 2.2. Brownian Motion. 2.3. The Poisson Process. 2.4. [alpha]-Stable Random Variables. 2.5. [alpha]-Stable Levy Motion -- 3. Computer Simulation of [alpha]-Stable Random Variables. 3.2. Computer Methods of Generation of Random Variables. 3.3. Series Representations of Stable Random Variables. 3.4. Convergence of LePage Random Series. 3.5. Computer Generation of [alpha]-Stable Distributions. 3.6. Exact Formula for Tail Probabilities. 3.7. Density Estimators -- 4. Stochastic Integration. 4.2. Ito Stochastic Integral. 4.3. [alpha]-Stable Stochastic Integrals of Deterministic Functions. 4.4. Infinitely Divisible Processes. 4.5. Stochastic Integrals with ID Integrators. 4.6. Levy Characteristics.
505 0 $a4.7. Stochastic Processes as Integrators. 4.8. Integrals of Deterministic Functions with ID Integrators. 4.9. Integrals with Stochastic Integrands and ID Integrators. 4.10. Diffusions Driven by Brownian Motion. 4.11. Diffusions Driven by [alpha]-Stable Levy Motion -- 5. Spectral Representations of Stationary Processes. 5.2. Gaussian Stationary Processes. 5.3. Representation of [alpha]-Stable Stochastic Processes. 5.4. Structure of Stationary Stable Processes. 5.5. Self-similar [alpha]-Stable Processes -- 6. Computer Approximations of Continuous Time Processes. 6.2. Approximation of Diffusions Driven by Brownian Motion. 6.3. Approximation of Diffusions Driven by [alpha]-Stable Levy Measure. 6.4. Examples of Application in Mathematics -- 7. Examples of [alpha]-Stable Stochastic Modeling. 7.1. Survey of [alpha]-Stable Modeling. 7.2. Chaos, Levy Flight, and Levy Walk. 7.3. Examples of Diffusions in Physics. 7.4. Logistic Model of Population Growth. 7.5. Option Pricing Model in Financial Economics.
505 0 $a8. Convergence of Approximate Methods. 8.2. Error of Approximation of Ito Integrals. 8.3. The Rate of Convergence of LePage Type Series. 8.4. Approximation of Levy [alpha]-Stable Diffusions. 8.5. Applications to Statistical Tests of Hypotheses. 8.6. Levy Processes and Poisson Random Measures. 8.7. Limit Theorems for Sums of i.i.d. Random Variables -- 9. Chaotic Behavior of Stationary Processes. 9.1. Examples of Chaotic Behavior. 9.2. Ergodic Property of Stationary Gaussian Processes. 9.3. Basic Facts of General Ergodic Theory. 9.4. Birkhoff Theorem for Stationary Processes. 9.5. Hierarchy of Chaotic Properties. 9.6. Dynamical Functional -- 10. Hierarchy of Chaos for Stable and ID Stationary Processes. 10.2. Ergodicity of Stable Processes. 10.3. Mixing and Other Chaotic Properties of Stable Processes. 10.4. Introduction to Stationary ID Processes. 10.5. Ergodic Properties of ID Processes. 10.6. Mixing Properties of ID Processes. 10.7. Examples of Chaotic Behavior of ID Processes.
505 0 $a10.8. Random Measures on Sequences of Sets -- Appendix: A Guide to Simulation.
520 $aThis practical reference/text presents new computer methods of approximation, simulation, and visualization for a host of [alpha]-stable stochastic processes and shows how [alpha]-stable variates are useful in the modeling of various problems arising in economics, finances, chemistry, physics, and engineering - providing accurate descriptions of real phenomena.
520 8 $aOffering detailed proofs for most of the results obtained, Simulation and Chaotic Behavior of [alpha]-Stable Stochastic Processes examines the properties of [alpha]-stable random variables and processes . . . supplies theoretical investigations and computer illustrations of the hierarchy of chaos for stochastic processes with applications to stochastic modeling . . . studies and characterizes the ergodic properties of different classes of stochastic processes . . . demonstrates how to apply the results obtained to a wide variety of disciplines . . . and more!
650 0 $aStochastic processes$xData processing.
700 1 $aWeron, A.$0http://id.loc.gov/authorities/names/n80115664
740 0 $aSimulation and chaotic behavior of alpha-stable stochastic processes.
830 0 $aMonographs and textbooks in pure and applied mathematics ;$v178.$0http://id.loc.gov/authorities/names/n42037163
852 00 $bmat$hQA274$i.J35 1994