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"Teori katastrofe menjelaskan bahwa perubahan kecil (smooth change) pada suatu parameter akan menyebabkan rusaknya kestabilan dan menimbulkan perubahan perilaku sistem yang drastis secara tiba-tiba. Dengan menggunakan kalkulus stokastik, fungsi delta Dirac, transformasi Fourier terhadap fungsi karakteristik serta persamaan Fokker-Planck, dapat dijelaskan hubungan antara model katastrofe cusp stokastik dengan suatu fungsi densitas probabilitas (FDP) stasioner. Pada tesis ini ditunjukkan bahwa model katastrofe cusp stokastik dapat digunakan untuk menjelaskan peristiwa krisis pasar saham, yaitu krisis Black Monday pada 19 Oktober 1987 di pasar saham Amerika. Estimasi parameter dengan metode momen menunjukkan bahwa terdapat perubahan nilai diskriminan Cardan dari positif ke negatif, sehingga menunjukkan adanya kasus perubahan FDP dari unimodal ke bimodal. Peristiwa katastrofe pada data Black Monday menunjukkan bahwa krisis ini dipengaruhi oleh faktor internal.

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Catastrophe theory explains that a smooth change of parameters can perturb the system stability to a sudden discontinuous state. Using stochastic calculus, Dirac delta function, Fourier transform of characteristic function, and Fokker-Planck equation we show the connection between stochastic cusp catastrophe model to a stationer probability density function (PDF).

This thesis shows that stochastic cusp catastrophe model can explains U.S stock market crash in October 19, 1987 called Black Monday. Parameter estimations using momen method shows change of Cardan discriminant from positive to negative which explain the stationer PDF in unimodal case to bimodal case. Catastrophe in Black Monday data explains that the crisis influenced by internal factor."

"This volume first introduces the mathematical tools necessary for understanding and working with a broad class of applied stochastic models. The toolbox includes Gaussian processes, independently scattered measures such as Gaussian white noise and Poisson random measures, stochastic integrals, compound Poisson, infinitely divisible and stable distributions and processes.Next, it illustrates general concepts by handling a transparent but rich example of a "teletraffic model". A minor tuning of a few parameters of the model leads to different workload regimes, including Wiener process, fractional Brownian motion and stable Levy process. The simplicity of the dependence mechanism used in the model enables us to get a clear understanding of long and short range dependence phenomena. The model also shows how light or heavy distribution tails lead to continuous Gaussian processes or to processes with jumps in the limiting regime. Finally, in this volume, readers will find discussions on the multivariate extensions that admit a variety of completely different applied interpretations."

"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."

"This self-contained monograph presents a new stochastic approach to global optimization problems arising in a variety of disciplines including mathematics, operations research, engineering, and economics. The volume deals with constrained and unconstrained problems and puts a special emphasis on large scale problems. It also introduces a new unified concept for unconstrained, constrained, vector, and stochastic global optimization problems. All methods presented are illustrated by various examples. Practical numerical algorithms are given and analyzed in detail. The topics presented include the randomized curve of steepest descent, the randomized curve of dominated points, the semi-implicit Euler method, the penalty approach, and active set strategies. The optimal decoding of block codes in digital communications is worked out as a case study and shows the potential and high practical relevance of this new approach."

"Learning english at Junior High School will master foyr skills ; listening ; speaking, reading. Make a match is one of the models in teching english that can help the students compose tthe text procedure materials well."

"Vocatinal school is one of the high schools that has been choen as priority for students after junior high school. But when they are not able to continue their study , they can make job field and invite others to work together. But in teaching and learning process, teachers still gate some problem. so, the teacher should more creative to apply more interesting methods for strategy. One of model is introduced by the writer, cooperative learning that is guessing word type. It is hoped that the model will help students."

"English is one of foreign language learned by junior high school students. learning consist of learning four integrated skills, listening , speaking, reading and writing .Writing is supposed to be the most difficult skill for the students. In this case the writer tried to use an approach in learning and teaching process, that is RDAS ( Read discuss arrange and stick)."