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"[This book is an introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. This textbook, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. Key topics include: Markov processes Stochastic differential equations Arbitrage-free markets and financial derivatives Insurance risk Population dynamics, and epidemics Agent-based models., This book is an introduction to the theory of continuous-time stochastic processes. A balance of theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, finance, and insurance using stochastic methods. This textbook, offers a rigorous and self-contained introduction to the theory of continuous-time stochastic processes, stochastic integrals, and stochastic differential equations. Expertly balancing theory and applications, the work features concrete examples of modeling real-world problems from biology, medicine, industrial applications, finance, and insurance using stochastic methods. Key topics include: Markov processes Stochastic differential equations Arbitrage-free markets and financial derivatives Insurance risk Population dynamics, and epidemics Agent-based models.]"

"While there are several texts on how to solve and analyze stochastic programs, this is the first text to address basic questions about how to model uncertainty, and how to reformulate a deterministic model so that it can be analyzed in a stochastic setting. This text would be suitable as a stand-alone or supplement for a second course in OR/MS or in optimization-oriented engineering disciplines where the instructor wants to explain where models come from and what the fundamental issues are. "

"Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems.Covering a wide range of areas of application of Markov processes, this second edition is revised to highlight the most important aspects as well as the most recent trends and applications of Markov processes. The author spent over 16 years in the industry before returning to academia, and he has applied many of the principles covered in this book in multiple research projects."

"ABSTRAKModel epidemik SIS (Susceptible Infected Susceptible) diaplikasikan dalampembuatan model matematis penyebaran penyakit influenza. Model penyebaranpenyakit flu dibuat dengan pendekatan stokastik. Model stokastik yang digunakandalam skripsi ini adalah model Continuous Time Markov Chain (CTMC). Padamodel CTMC, dikonstruksi probabilitas transisi, ekspektasi, dan limit distribusidari banyaknya individu yang terinfeksi penyakit flu dengan asumsi banyaknyaindividu terinfeksi hanya dapat bertambah satu, berkurang satu atau tetap dalaminterval waktu yang sangat pendek (
t 􀀀 0). Ekspektasi dari banyaknya individuyang terinfeksi flu tidak dapat diselesaikan secara langsung, tetapi dapat diketahuibahwa rata- rata pada model stokastik lebih kecil dibandingkan dengan solusideterministik. Dari kajian tentang limit distribusi, didapatkan bahwa probabilitastidak ada individu terinfeksi adalah satu saat t 􀀀 ª. Simulasi numerik padapenyebaran penyakit flu diberikan sebagai pendukung untuk interpretasi model

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ABSTRACTMathematical model for the spread of influenza using SIS (Susceptible InfectedSusceptible) Epidemic Model for constant total human population size is discussedin this undergraduate thesis. These influenza model was made with stochasticapproach. Stochastic model that used in this thesis is Continuous Time MarkovChain (CTMC). Transition probability, expectation, and limiting distribution forthe number of infected people were constructed in CTMC with assumption that thenumber of infected people might change by increasing one, decreasing one, or stillin the time interval that tends to zero (
t 􀀀 0). The expectation for the number ofinfected people cannot be solved directly, but we will know that the mean of thestochastic SIS epidemic model is less than the deterministic solution. Fromlimiting distribution analyses, probability that there are no infected people att 􀀀 ª is one. Some numerical simulation for the spread of influenza is given togive a better interpretation and a better understanding about the modelinterpretation"

"This book develops systematically and rigorously, yet in an expository and lively manner, the evolution of general random processes and their large time properties such as transience, recurrence, and convergence to steady states. The emphasis is on the most important classes of these processes from the viewpoint of theory as well as applications, namely, Markov processes."

"This is the expanded second edition of a successful textbook that provides a broad introduction to important areas of stochastic modelling. The original text was developed from lecture notes for a one-semester course for third-year science and actuarial students at the University of Melbourne. It reviewed the basics of probability theory and then covered the following topics: Markov chains, Markov decision processes, jump Markov processes, elements of queueing theory, basic renewal theory, elements of time series and simulation. The present edition adds new chapters on elements of stochastic calculus and introductory mathematical finance that logically complement the topics chosen for the first edition. This makes the book suitable for a larger variety of university courses presenting the fundamentals of modern stochastic modelling. Instead of rigorous proofs we often give only sketches of the arguments, with indications as to why a particular result holds and also how it is related to other results, and illustrate them by examples. Wherever possible, the book includes references to more specialised texts on respective topics that contain both proofs and more advanced material.Readership: Advanced undergraduates, graduate students, lecturers and researchers in mathematics, statistics, actuarial sciences and economics."

"The monograph addresses a problem of stochastic analysis based on the uncertainty assessment by simulation and application of this method in ecology and steel industry under uncertainty. "