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"Selected papers submitted by participants of the international Conference “Stochastic Analysis and Applied Probability 2010” ( www.saap2010.org ) make up the basis of this volume. The SAAP 2010 was held in Tunisia, from 7-9 October, 2010, and was organized by the “Applied Mathematics & Mathematical Physics” research unit of the preparatory institute to the military academies of Sousse (Tunisia), chaired by Mounir Zili. The papers cover theoretical, numerical and applied aspects of stochastic processes and stochastic differential equations. The study of such topic is motivated in part by the need to model, understand, forecast and control the behavior of many natural phenomena that evolve in time in a random way. Such phenomena appear in the fields of finance, telecommunications, economics, biology, geology, demography, physics, chemistry, signal processing and modern control theory, to mention just a few. As this book emphasizes the importance of numerical and theoretical studies of the stochastic differential equations and stochastic processes."

"The emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Volume 2 builds on the fundamentals presented in Volume 1, delving deeper into relationships among stochastic geometry, geometric aspects of the theory of communications and coding, multivariate statistical analysis, and error propagation on Lie groups. Extensive exercises, motivating examples, and real-world applications make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry."

"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."

"Tingkat mortalitas merupakan komponen penting dalam analisis kesehatan masyarakat yang diperlukan oleh banyak institusi seperti pemerintah, organisasi kesehatan, hingga perusahaan asuransi. Akan tetapi, data tingkat mortalitas merupakan data yang terus berubah seiring berjalannya waktu sehingga dibutuhkan peramalan tingkat mortalitas. Untuk melakukan peramalan tingkat mortalitas, diperlukan kesesuaian dari berbagai metode dan model untuk dapat memaksimalkan tingkat akurasi dari nilai hasil ramalan. Untuk mencapai hal tersebut, skripsi ini melakukan simulasi peramalan dengan model Cairns-Blake-Dowd (CBD) yang diaplikasikan terhadap data Tingkat Mortalitas Indonesia untuk jenis kelamin laki-laki yang bersifat tahunan. Model CBD sendiri memiliki dua parameter yang diestimasi menggunakan metode Least Square. Lalu, dikarenakan sifat parameter yang merupakan deret waktu multivariat, akan digunakan metode peramalan berupa Vector Autoregressive Integrated Moving Average (VARIMA). Hasil ramalan tersebut kemudian disubstitusikan kembali ke dalam model CBD untuk mendapatkan nilai tingkat mortalitas pada tahun-tahun berikutnya. Dalam menentukan akurasi hasil peramalan dari metode VARIMA dan estimasi parameter dari metode Least Square tersebut, digunakan metode Mean Squared Error (MSE).

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Mortality rate is a crucial component in the analysis of public health which is required by various institutions such as the government, health organizations, and insurance companies. However, mortality rate data is constantly changing over time, necessitating the forecasting of mortality rates. Therefore, to forecast mortality rates, the alignment of various methods and models is necessary to maximize the accuracy of the forecasted values. To achieve this, this thesis will conduct a forecasting simulation using the Cairns-Blake-Dowd (CBD) model applied to Indonesian Mortality Rate data for males on an annual basis. The CBD model itself has two parameters to be estimated using the Least Square method. Then, due to the nature of the parameters as a multivariate time series, the Vector Autoregressive Integrated Moving Average (VARIMA) forecasting method will be employed. The forecasted results will be substituted back into the CBD model to obtain mortality rate values for the upcoming years. In determining the accuracy of the forecasting results from VARIMA and estimation from Least Square, the Mean Squared Error (MSE) method will be utilized."

"This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science for a clear presentation of stochastic processes and control for jump diffusions in continuous time. The author covers the important problem of controlling these systems and, through the use of a jump calculus construction, discusses the strong role of discontinuous and nonsmooth properties versus random properties in stochastic systems. The book emphasizes modeling and problem solving and presents sample applications in financial engineering and biomedical modeling. Computational and analytic exercises and examples are included throughout. While classical applied mathematics is used in most of the chapters to set up systematic derivations and essential proofs, the final chapter bridges the gap between the applied and the abstract worlds to give readers an understanding of the more abstract literature on jump diffusions."

"Uncertainty and risk are integral to engineering because real systems have inherent ambiguities that arise naturally or due to our inability to model complex physics. The authors discuss probability theory, stochastic processes, estimation, and stochastic control strategies and show how probability can be used to model uncertainty in control and estimation problems. The material is practical and rich in research opportunities.The authors provide a comprehensive treatment of stochastic systems from the foundations of probability to stochastic optimal control. The book covers discrete- and continuous-time stochastic dynamic systems leading to the derivation of the Kalman filter, its properties, and its relation to the frequency domain Wiener filter as well as the dynamic programming derivation of the linear quadratic Gaussian (LQG) and the linear exponential Gaussian (LEG) controllers and their relation to H2 and H controllers and system robustness.Stochastic Processes, Estimation, and Control is divided into three related sections. First, the authors present the concepts of probability theory, random variables, and stochastic processes, which lead to the topics of expectation, conditional expectation, and discrete-time estimation and the Kalman filter. After establishing this foundation, stochastic calculus and continuous-time estimation are introduced. Finally, dynamic programming for both discrete-time and continuous-time systems leads to the solution of optimal stochastic control problems, resulting in controllers with significant practical application."

"ABSTRAKOptimalisasi Stokastik Tindakan Pencegahan Resiko Rantai Suplai-Sebuah Metodologi untuk Meningkatkan Ketahanan Suplai Bahan Bakar Minyak Bersubsidi di Indonesia. Metode berdasarkan simulasi Monte Carlo untuk opimasi stokastik pada penilaian risiko diperlukan untuk menyelesaikan masalah kompleks di dalam jaminan ketersediaan bahan bakar bersubsidi di Indonesia.Untuk mengatasi kendala distribusi BBM bersubsidi di Indonesia yang memiliki populasi penduduk keempat terpadat di dunia lebih dari 250.000.000 jiwa dengan 66,5 populasi masyarakat produktif, dan memiliki lebih dari 17.000 pulau dengan populasi penduduk yang terpusat hanya di wilayah ibukota Negara diperlukan system pengawasan dan penanganan risiko yang terukur serta terintegrasi demi jaminan ketersediaan BBM bersubsidi. Dengan mempertimbangkan masalah kompleks tersebut, penelitian ini sangat dipengaruhi oleh ketidakpastian dan probabilitas.Oleh karena itu, penelitian ini menggunakan metode simulasi optimasi stokastik berdasarkan sampling Monte Carlo pada kerangka kerja analisis risiko dengan keterbaruan parameter ldquo;FIRST rdquo;, yang dikombinasi dengan Analisis Sensitifitas untuk menentukan prioritas penanganan mitigasi risiko yang terintegrasi agar implikasi dari rancangan model yang baru dari penelitian ini dapat memberikan waktu mitigasi yang lebih cepat.Hasil dari penelitian ini dapat mengidentifikasi ide-ide inovatif pada audit berdasarkan risiko pada manajemen risiko rantai pasok dan parameter FIRST Fairness, Independence, Reliable, Sustainable, Transparent dalam penilaian risiko. Selain itu, integrasi pada analisis risiko menghasilkan tingkatan prioritas pada analisis sensitivitas dengan temuan yang menunjukkan bahwa waktu mitigasi yang baru lebih cepat sebanyak 60 dari waktu mitigasi risiko dengan metode yang umum.Kata kunci: faktor ldquo;FIRST rdquo;; Sampling Monte Carlo; Simulasi stokastik; ketahanan pasokan, keamanan, tingkat perubahan.

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ABSTRACTMonte Carlo simulation based methods for stochastic optimization of risk measures is required to solve complex problems in supply security of subsidized fuel oil in Indonesia. In order to overcome constraints in distribution of subsidized fuel in Indonesia, which has the fourth largest population in the world mdash more than 250,000,000 people with 66.5 of productive population, and has more than 17,000 islands with its population centered around the nation 39 s capital only mdash it is necessary to have a measurable and integrated risk analysis with monitoring system for the purpose of supply security of subsidized fuel. In consideration of this complex issue, uncertainty and probability heavily affected this research. Therefore, this research did the Monte Carlo sampling based stochastic simulation optimization with the state of the art FIRST parameter combined with the Sensitivity Analysis to determine the priority of integrated risk mitigation handling so that the implication of the new model design from this research may give faster risk mitigation time. The results of the research identified innovative ideas of risk based audit on supply chain risk management and new FIRST Fairness, Independence, Reliable, Sustainable, Transparent parameters on risk measures. In addition to that, the integration of risk analysis confirmed the innovative level of priority on sensitivity analysis. Moreover, the findings showed that the new risk mitigation time was 60 faster than the original risk mitigation time.Keywords FIRST factor Monte Carlo sampling Stochastic simulation Supply security, rate of change"