LEADER 04162nam 22005295 450 001 9910254291403321 005 20200701021746.0 010 $a3-319-50038-4 024 7 $a10.1007/978-3-319-50038-6 035 $a(CKB)3710000001079873 035 $a(DE-He213)978-3-319-50038-6 035 $a(MiAaPQ)EBC5594464 035 $a(PPN)198869231 035 $a(EXLCZ)993710000001079873 100 $a20170201d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic Modeling /$fby Nicolas Lanchier 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XIII, 303 p. 63 illus., 6 illus. in color.) 225 1 $aUniversitext,$x0172-5939 311 $a3-319-50037-6 320 $aIncludes bibliographical references and index. 327 $a1. Basics of Measure and Probability Theory -- 2. Distribution and Conditional Expectation -- 3. Limit Theorems -- 4. Stochastic Processes: General Definition -- 5. Martingales -- 6. Branching Processes -- 7. Discrete-time Markov Chains -- 8. Symmetric Simple Random Walks -- 9. Poisson Point and Poisson Processes -- 10. Continuous-time Markov Chains -- 11. Logistic Growth Process -- 12. Wright-Fisher and Moran Models -- 13. Percolation Models -- 14. Interacting Particle Systems -- 15. The Contact Process -- 16. The Voter Model -- 17. Numerical Simulations in C and Matlab. 330 $aThree coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the gambler?s ruin chain, branching processes, symmetric random walks, and queueing systems. The third, more research-oriented part of the text, discusses special stochastic processes of interest in physics, biology, and sociology. Additional emphasis is placed on minimal models that have been used historically to develop new mathematical techniques in the field of stochastic processes: the logistic growth process, the Wright?Fisher model, Kingman?s coalescent, percolation models, the contact process, and the voter model. Further treatment of the material explains how these special processes are connected to each other from a modeling perspective as well as their simulation capabilities in C and Matlab?. 410 0$aUniversitext,$x0172-5939 606 $aProbabilities 606 $aMathematical models 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068 615 0$aProbabilities. 615 0$aMathematical models. 615 14$aProbability Theory and Stochastic Processes. 615 24$aMathematical Modeling and Industrial Mathematics. 676 $a003.76 700 $aLanchier$b Nicolas$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767446 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254291403321 996 $aStochastic Modeling$91562401 997 $aUNINA