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"The thesis deals with averaging dynamics in a multiagent networked system, which is a main mechanism for diffusing the information over such networks. It arises in a wide range of applications in engineered physical networks (such as mobile communication and sensor networks), as well as social and economic networks. The thesis provides in depth study of stability and other phenomena characterizing the limiting behavior of both deterministic and random averaging dynamics. By developing new concepts, and using the tools from dynamic system theory and non-negative matrix theory, several novel fundamental results are rigorously developed. These contribute significantly to our understanding of averaging dynamics as well as to non-negative random matrix theory."

"This book treats methods inspired by attempts to understand the seemingly non-mathematical question of bacterial chemotaxis and their application in other environments. The text presents significant generalizations on existing stochastic averaging theory developed from scratch and necessitated by the need to avoid violation of previous theoretical assumptions by algorithms which are otherwise effective in treating these systems. Coverage is given to four main topics. Stochastic averaging theorems are developed for the analysis of continuous-time nonlinear systems with random forcing, removing prior restrictions on nonlinearity growth and on the finiteness of the time interval. The new stochastic averaging theorems are usable not only as approximation tools but also for providing stability guarantees. Stochastic extremum-seeking algorithms are introduced for optimization of systems without available models. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms for non-cooperative/adversarial games is described. The analysis of their convergence to Nash equilibria is provided. The algorithms are illustrated on models of economic competition and on problems of the deployment of teams of robotic vehicles. Bacterial locomotion, such as chemotaxis in E. coli, is explored with the aim of identifying two simple feedback laws for climbing nutrient gradients. Stochastic extremum seeking is shown to be a biologically-plausible interpretation for chemotaxis. For the same chemotaxis-inspired stochastic feedback laws, the book also provides a detailed analysis of convergence for models of nonholonomic robotic vehicles operating in GPS-denied environments. The book contains block diagrams and several simulation examples, including examples arising from bacterial locomotion, multi-agent robotic systems, and economic market models. Stochastic averaging and extremum seeking will be informative for control engineers from backgrounds in electrical, mechanical, chemical and aerospace engineering and to applied mathematicians. Economics researchers, biologists, biophysicists and roboticists will find the applications examples instructive."

"Model-model Persamaan Diferensial Stokastik (PDS) memiliki peranan yang sangat penting di berbagai bidang industri, misalnya ekonomi, keuangan, biologi, kimia, epidemiologi, juga mikroelektronik (Higham D. J., 2001). Metode numerik seringkali digunakan untuk mengaproksimasi solusi dari suatu model PDS, sehingga dibutuhkan suatu proses komputasi untuk memperoleh solusi dari suatu model PDS tersebut. Model-model PDS biasanya melibatkan data dalam jumlah besar ataupun proses komputasi yang banyak, sehingga berdampak pada waktu komputasi yang semakin lama. Untuk mempercepat waktu komputasi, maka diterapkan komputasi paralel. Komputasi paralel adalah salah satu teknik melakukan komputasi secara bersamaan dengan memanfaatkan beberapa komputer/prosesor pada suatu waktu tertentu.Dalam skripsi ini diberikan algoritma paralel untuk mengaproksimasi solusi dari suatu model PDS. Algoritma-algoritma ini diimplementasikan dalam program yang dijalankan pada mesin multicore dengan MATLAB dan Parallel Computing Toolbox (versi trial). Diberikan juga kinerja algoritma paralel yang diukur dengan speed up dan efisiensi paralel.

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Stochastic Differential Equations (SDEs) models play a prominent role in a range of application areas, including biology, chemistry, epidemiology, mechanics, microelectronics, economics, and finance (Higham D. J., 2001). Numerical method is usually used to get an approximate solution of SDEs models which often involve huge data or many computation steps, hence need more computation time. Parallel computing is an alternative that can reduce the computation time.

This skripsi discuss some parallel techniques to solve SDEs problems especially in finance models. The parallel techniques is designed to utilize several processors simultaneously. In this case the algorithms run on multicore machine with MATLAB and Parallel Computing Toolbox (trial version). Parallel perfomance of the algorithms are also given which compared the speed up and efficiency of several parallel techniques."

"A systematic, self-contained treatment of the theory of stochastic differential equations in infinite dimensional spaces. Included is a discussion of Schwartz spaces of distributions in relation to probability theory and infinite dimensional stochastic analysis, as well as the random variables and stochastic processes that take values in infinite dimensional spaces."

"Penelitian tentang model persediaan telah banyak dilakukan dan menjadi solusi bagi perusahaan dalam menghadapi ketidakpastiaan dari permintaan pelanggan. Selain data permintaan yang bersifat stokastik, sering pula ditemukan leadtime kedatangan bahan baku di suatu perusahaan yang bersifat stokastik. Sering kali leadtime yang bersifat stokastik dihitung menjadi leadtime yang tetap untuk menyederhanakan perhitungan dan perancangan model persediaan. Hal ini dapat memicu terjadinya stockout pada kenyataan di lapangan, karena tidak memperhitungkan kejadian leadtime kedatangan bahan baku yang berubah atau tidak tetap seperti yang ditentukan. Sehingga penelitian ini dibuat untuk menganalisis bagaimana pengaruh leadtime yang bersifat stokastik pada performa sistem persediaan di suatu perusahaan manufaktur perusahaan di Indonesia. Penelitian ini menggunakan simulasi Monte Carlo untuk melakukan RNG data berjumlah 5000 periode. Simulasi Monte Carlo dipilih karena data permintaan kebutuhan bahan baku komponen pehiasan tidak mengikuti distribusi normal. Dalam penelitian ini juga akan memakai model persediaan (R,Q) untuk membandingkan total biaya yang dikeluarkan ketika menggunakan model persediaan dengan leadtime stokastik atau menggunakan model persediaan dengan leadtime tetap.

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Research on the inventory model has been done a lot and is a solution for companies in dealing with uncertainty of customer demand. In addition to stochastic demand data, it is often found the lead time for the arrival of raw materials in a company that is stochastic. Often a stochastic leadtime is calculated to be a fixed leadtime to simplify the calculation and design of the inventory model. This can trigger a stockout in reality, because it does not calculate the occurrence of the lead time for the arrival of raw materials that changes or does not remain as determined. So this research was made to analyze how the effect of stochastic leadtime on the performance of the inventory system in a manufacturing company in Indonesia. This study uses a Monte Carlo simulation to perform RNG data totaling 5000 periods. The Monte Carlo simulation was chosen because the data on the demand for the raw material requirements of the decking components did not follow a normal distribution. In this study, we will also use the inventory model (R, Q) to compare the total costs incurred when using an inventory model with stochastic leadtime or using an inventory model with a fixed leadtime."

"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."