Markov processes provide very flexible, powerful, and efficient means for the description and analysis of dynamic (computer) system properties. Performance and dependability measures can be easily derived. Moreover, Markov processes constitute the fundamental theory underlying the concept of queueing systems. In fact, the notation of queueing systems has been viewed sometimes as a high-level specification technique for (a sub-class of) Markov processes.
Steady-State Solutions of Markov Chains
In this chapter, we restrict ourselves to the computation of the steady-state probability vector’ of ergo&c Markov chains. Most of the literature on solution techniques of Markov chains assumes ergodicity of the underlying model. A comprehensive source on algorithms for steady-state solution techniques is the book by Stewart [Stew94]. From Eq. (2.15) and Eq. (2.58), we have v = VP and 0 = nQ, respectively, as points of departure for the study of steady-state solution techniques. Eq. (2.15) can be transformed so that: 0 = Y(P -1).
This book aims to give a complete and self-contained presentation of semi-
Markov models with finitely many states, in view of solving real life problems of
risk management in three main fields: Finance, Insurance and Reliability
providing a useful complement to our first book (Janssen and Manca (2006))
which gives a theoretical presentation of semi-Markov theory. However, to help
assure the book is self-contained, the first three chapters provide a summary of
the basic tools on semi-Markov theory that the reader will need to understand our
In this section we introduce an efficient method for the steady-state analysis of Markov chains. Whereas direct and iterative techniques can be used for the exact analysis of Markov chains as previously discussed, the method computations of Courtois [Cour75, Cour77] is mainly applied to approximate u NN the desired state probability vector u. Courtois’s approach is based of on decomposability properties of the models under consideration.
Transient Solution of Markov Chains
Transient solution is more meaningful than steady-state solution when the system under investigation needs to be evaluated with respect to its shortterm behavior, Using steady-state measures instead of transient measures could lead to substantial errors in this case. Furthermore, applying transient analysis is the onl y choice if non-ergodic models are investigated, Transient analysis of Markov chains has been attracting increasing attention and is of particular importance in dependability modeling. ...
This chapter considers several large applications. The set of applications organized into three sections. In Section 13.1, we present case studies queueing network applications. In Section 13.2 we present case studies Markov chains and stochastic Petri nets. In Section 13.3, case studies hierarchical models are presented.
This book is an extension of “Probability for Finance” to multi-period financial models, either in the discrete or continuous-time framework. It describes the most important stochastic processes used in finance in a pedagogical way, especially Markov chains, Brownian motion and martingales. It also shows how mathematical tools like filtrations, Itô’s lemma or Girsanov theorem should be understood in the framework of financial models. It also provides many illustrations coming from the financial literature....
Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Some limit theorems for the second-order Markov chains indexed by a general infinite tree with uniform bounded degree
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Some Shannon-McMillan Approximation Theorems for Markov Chain Field on the Generalized Bethe Tree
This paper describes an unsupervised dynamic graphical model for morphological segmentation and bilingual morpheme alignment for statistical machine translation. The model extends Hidden Semi-Markov chain models by using factored output nodes and special structures for its conditional probability distributions. It relies on morpho-syntactic and lexical source-side information (part-of-speech, morphological segmentation) while learning a morpheme segmentation over the target language. Our model outperforms a competitive word alignment system in alignment quality. ...
The effective application of Markov chains has been paid much attention, and it has
raised a lot of theoretical and applied problems. In this paper, we would like to approach one of these problems which is finding the long-run behavior of extremely huge-state Markov chains according to the direction of investigating the structure of Markov Graph to reduce complexity of computation. We focus on the way to access to the finite-state Markov chain theory via Graph theory.
We would like to draw attention to Hidden Markov Tree Models (HMTM), which are to our knowledge still unexploited in the ﬁeld of Computational Linguistics, in spite of highly successful Hidden Markov (Chain) Models. In dependency trees, the independence assumptions made by HMTM correspond to the intuition of linguistic dependency. Therefore we suggest to use HMTM and tree-modiﬁed Viterbi algorithm for tasks interpretable as labeling nodes of dependency trees.
Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí y học Molecular Biology cung cấp cho các bạn kiến thức về ngành sinh học đề tài: Effective p-value computations using Finite Markov Chain Imbedding (FMCI): application to local score and to pattern statistics...
Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí y học Molecular Biology cung cấp cho các bạn kiến thức về ngành sinh học đề tài: Pattern statistics on Markov chains and sensitivity to parameter estimation...
(Ứng dụng mô hình Cellular Automaton Markov để dự báo và đánh giá biến đổi sử dụng đất trong lưu vực sông Nakdong, Hàn Quốc) Nghiên cứu dự báo và đánh giá biến đổi sử dụng đất trong tương lai không chỉ có vai trò quan trọng trong đánh giá các thay đổi của sử dụng đất mà còn có ý nghĩa lớn lao trong công tác quản lý và sử dụng tài nguyên đất, tài nguyên nước trong lưu vực một cách hiệu quả.
Contents 9 Sample path properties of local times 9.1 Bounded discontinuities 9.2 A necessary condition for unboundedness 9.3 Suﬃcient conditions for continuity 9.4 Continuity and boundedness of local times 9.5 Moduli of continuity 9.6 Stable mixtures 9.7 Local times for certain Markov chains 9.8 Rate of growth of unbounded local times 9.9 Notes and references p-variation 10.1 Quadratic variation of Brownian motion 10.2 p-variation of Gaussian processes 10.3 Additional variational results for Gaussian processes 10.4 p-variation of local times 10.
Probabilistic inference is an attractive approach to uncertain reasoning and empirical
learning in artificial intelligence. Computational difficulties arise, however,
because probabilistic models with the necessary realism and
exibility lead to complex
distributions over high-dimensional spaces.