Markov Models
نویسنده
چکیده
1 Stochastic processes A stochastic process is an indexed collection of random variables, {Xt}, t ∈ T . If the index set T is discrete, we will often write t ∈ {1, 2, . . .}, to represent discrete time steps. For a finite number of variables, we will assume t ∈ 1 : d as usual, where d is the length of the sequence. If the state space X is finite, we will write Xt ∈ {1, 2, . . . ,K}, where K is the number of states. If the state space is countably infinite, we will write Xt ∈ {0, 1, 2, . . .}. If the state space is continuous, we will write Xt ∈ IR, although Xt could also be a vector. Here are some examples of stochastic processes: • A finite sequence of i.i.d. discrete random variables, {X1, X2, . . . , Xn}, where Xt ∈ {1, . . . ,K}. This is discrete (finite) time and discrete (finite) state. • An infinite sequence of non i.i.d. random variables {X1, X2, . . .}, Xt ∈ IR, representing, for example, the daily temperature or stock price. This is discrete time but continuous state. • An infinite sequence of non i.i.d. random variables {X1, X2, . . .}, Xt ∈ {0, 1, 2, . . .}, representing, for example, the number of people in a queue at time t. This is discrete time and discrete state. • Brownian motion, which models a particle performing a Gaussian random walk along the real line. This is continuous-time and continuous-state. For the rest of this Chapter, we shall restrict attention to discrete-time, discrete-state stochastic processes. 2 Markov chains Recall that for any set of random variables X1, . . . , Xd, we can write the joint density using the chain rule as
منابع مشابه
Introducing Busy Customer Portfolio Using Hidden Markov Model
Due to the effective role of Markov models in customer relationship management (CRM), there is a lack of comprehensive literature review which contains all related literatures. In this paper the focus is on academic databases to find all the articles that had been published in 2011 and earlier. One hundred articles were identified and reviewed to find direct relevance for applying Markov models...
متن کاملApplying Semi-Markov Models for forecasting the Triple Dimensions of Next Earthquake Occurrences: with Case Study in Iran Area
In this paper Semi-Markov models are used to forecast the triple dimensions of next earthquake occurrences. Each earthquake can be investigated in three dimensions including temporal, spatial and magnitude. Semi-Markov models can be used for earthquake forecasting in each arbitrary area and each area can be divided into several zones. In Semi-Markov models each zone can be considered as a sta...
متن کاملAsymmetric Effects of Monetary Policy and Business Cycles in Iran using Markov-switching Models
This paper investigates the asymmetric effects of monetary policy on economic growth over business cycles in Iran. Estimating the models using the Hamilton (1989) Markov-switching model and by employing the data for 1960-2012, the results well identify two regimes characterized as expansion and recession. Moreover, the results show that an expansionary monetary policy has a positive and statist...
متن کاملSpeaker Independent Speech Recognition Using Hidden Markov Models for Persian Isolated Words
متن کامل
Estimating Stock Price in Energy Market Including Oil, Gas, and Coal: The Comparison of Linear and Non-Linear Two-State Markov Regime Switching Models
A common method to study the dynamic behavior of macroeconomic variables is using linear time series models; however, they are unable to explain nonlinear behavior of the series. Given the dependency between stock market and derivatives, the behavior of the underlying asset price can be modeled using Markov switching process properties and the economic regime significance. In this paper, a two-...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006