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Examples Of Markov Chains
This article contains examples of Markov chains and Markov processes in action. All examples are in the countable state space. For an overview of Markov chains in general state space, see Markov chains on a measurable state space. Discrete-time Board games played with dice A game of snakes and ladders or any other game whose moves are determined entirely by dice is a Markov chain, indeed, an absorbing Markov chain. This is in contrast to card games such as blackjack, where the cards represent a 'memory' of the past moves. To see the difference, consider the probability for a certain event in the game. In the above-mentioned dice games, the only thing that matters is the current state of the board. The next state of the board depends on the current state, and the next roll of the dice. It doesn't depend on how things got to their current state. In a game such as blackjack, a player can gain an advantage by remembering which cards have already been shown (and hence which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Chain
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairs ''now''." A countably infinite sequence, in which the chain moves state at discrete time steps, gives a discrete-time Markov chain (DTMC). A continuous-time process is called a continuous-time Markov chain (CTMC). It is named after the Russian mathematician Andrey Markov. Markov chains have many applications as statistical models of real-world processes, such as studying cruise control systems in motor vehicles, queues or lines of customers arriving at an airport, currency exchange rates and animal population dynamics. Markov processes are the basis for general stochastic simulation methods known as Markov chain Monte Carlo, which are used for simulating sampling from complex probability dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
State Transition
State may refer to: Arts, entertainment, and media Literature * ''State Magazine'', a monthly magazine published by the U.S. Department of State * ''The State'' (newspaper), a daily newspaper in Columbia, South Carolina, United States * ''Our State'', a monthly magazine published in North Carolina and formerly called ''The State'' * The State (Larry Niven), a fictional future government in three novels by Larry Niven Music Groups and labels * States Records, an American record label * The State (band), Australian band previously known as the Cutters Albums * ''State'' (album), a 2013 album by Todd Rundgren * ''States'' (album), a 2013 album by the Paper Kites * ''States'', a 1991 album by Klinik * ''The State'' (album), a 1999 album by Nickelback Television * ''The State'' (American TV series), 1993 * ''The State'' (British TV series), 2017 Other * The State (comedy troupe), an American comedy troupe Law and politics * State (polity), a centralized political organizati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stochastic Cellular Automata
Stochastic cellular automata or probabilistic cellular automata (PCA) or random cellular automata or locally interacting Markov chains are an important extension of cellular automaton. Cellular automata are a discrete-time dynamical system of interacting entities, whose state is discrete. The state of the collection of entities is updated at each discrete time according to some simple homogeneous rule. All entities' states are updated in parallel or synchronously. Stochastic Cellular Automata are CA whose updating rule is a stochastic one, which means the new entities' states are chosen according to some probability distributions. It is a discrete-time random dynamical system. From the spatial interaction between the entities, despite the simplicity of the updating rules, complex behaviour may emerge like self-organization. As mathematical object, it may be considered in the framework of stochastic processes as an interacting particle system in discrete-time. See for a more deta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interacting Particle System
In probability theory, an interacting particle system (IPS) is a stochastic process (X(t))_ on some configuration space \Omega= S^G given by a site space, a countable-infinite graph G and a local state space, a compact metric space S . More precisely IPS are continuous-time Markov jump processes describing the collective behavior of stochastically interacting components. IPS are the continuous-time analogue of stochastic cellular automata. Among the main examples are the voter model, the contact process, the asymmetric simple exclusion process (ASEP), the Glauber dynamics and in particular the stochastic Ising model. IPS are usually defined via their Markov generator giving rise to a unique Markov process using Markov semigroups and the Hille-Yosida theorem. The generator again is given via so-called transition rates c_\Lambda(\eta,\xi)>0 where \Lambda\subset G is a finite set of sites and \eta,\xi\in\Omega with \eta_i=\xi_i for all i\notin\Lambda. The rates describe ex ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mark V
Mark V or Mark 5 often refers to the fifth version of a product, frequently military hardware. "Mark", meaning "model" or "variant", can be abbreviated "Mk." Mark V or Mark 5 can specifically refer to: In technology In military and weaponry * BL 13.5 inch Mk V naval gun (1912); British gun that was a defining feature of the super-dreadnought ''Orion''-class battleships * QF 4 inch Mk V naval gun (1914); British naval gun used for coastal defense and anti-aircraft * Mark V tank, a series of variations of the World War I Mark I tank ** Mark V Composite tank in Estonian service; specific design and service of the Mark V tank as used by Estonia * BL 8-inch howitzer Mk I – V; World War I British gun, heavy and short-range * Mk 5 mine (1943); British anti-tank mine used in World War II * Supermarine Spitfire Mk V; 1941 British fighter aircraft augmented with high-altitude capability * Mark 5 nuclear bomb (1952–1963); American nuclear bomb * Mark V Special Operations Craft (1995), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Poisson Point Process
In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field. This point process has convenient mathematical properties, which has led to its being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as astronomy,G. J. Babu and E. D. Feigelson. Spatial point processes in astronomy. ''Journal of statistical planning and inference'', 50(3):311–326, 1996. biology,H. G. Othmer, S. R. Dunbar, and W. Alt. Models of dispersal in biological systems. ''Journal of mathematical biology'', 26(3):263–298, 1988. ecology,H. Thompson. Spatial point processes, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous-time Markov Process
A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential random variable and then move to a different state as specified by the probabilities of a stochastic matrix. An equivalent formulation describes the process as changing state according to the least value of a set of exponential random variables, one for each possible state it can move to, with the parameters determined by the current state. An example of a CTMC with three states \ is as follows: the process makes a transition after the amount of time specified by the holding time—an exponential random variable E_i, where ''i'' is its current state. Each random variable is independent and such that E_0\sim \text(6), E_1\sim \text(12) and E_2\sim \text(18). When a transition is to be made, the process moves according to the jump chain, a discrete-time Markov chain with stochastic matrix: :\begin 0 & \frac & \frac \\ \frac & ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Distribution
In probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts. The exponential distribution is not the same as the class of exponential families of distributions. This is a large class of probability distributions that includes the exponential distribution as one of its members, but also includes many other distributions, like the normal, binomial, gamma, and Poisson distributions. Definitions Probability density function The probability density function (pdf) of an exponential distribution is : f(x;\lambda) = \begin \lambda ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independent And Identically Distributed Random Variables
In probability theory and statistics, a collection of random variables is independent and identically distributed if each random variable has the same probability distribution as the others and all are mutually independent. This property is usually abbreviated as ''i.i.d.'', ''iid'', or ''IID''. IID was first defined in statistics and finds application in different fields such as data mining and signal processing. Introduction In statistics, we commonly deal with random samples. A random sample can be thought of as a set of objects that are chosen randomly. Or, more formally, it’s “a sequence of independent, identically distributed (IID) random variables”. In other words, the terms ''random sample'' and ''IID'' are basically one and the same. In statistics, we usually say “random sample,” but in probability it’s more common to say “IID.” * Identically Distributed means that there are no overall trends–the distribution doesn’t fluctuate and all items in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite-state Machine
A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number of '' states'' at any given time. The FSM can change from one state to another in response to some inputs; the change from one state to another is called a ''transition''. An FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types— deterministic finite-state machines and non-deterministic finite-state machines. A deterministic finite-state machine can be constructed equivalent to any non-deterministic one. The behavior of state machines can be observed in many devices in modern society that perform a predetermined sequence of actions depending on a sequence of events with which they are presented. Simple examples are vending machines, which dispense p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Chains Prediction On 50 Discrete Steps
Markov (Bulgarian, russian: Марков), Markova, and Markoff are common surnames used in Russia and Bulgaria. Notable people with the name include: Academics *Ivana Markova (born 1938), Czechoslovak-British emeritus professor of psychology at the University of Stirling * John Markoff (sociologist) (born 1942), American professor of sociology and history at the University of Pittsburgh *Konstantin Markov (1905–1980), Soviet geomorphologist and quaternary geologist Mathematics, science, and technology *Alexander V. Markov (1965-), Russian biologist *Andrey Markov (1856–1922), Russian mathematician *Vladimir Andreevich Markov (1871–1897), Russian mathematician, brother of Andrey Markov (Sr.) * Andrey Markov Jr. (1903–1979), Russian mathematician and son of Andrey Markov *John Markoff (born 1949), American journalist of computer industry and technology *Moisey Markov (1908–1994), Russian physicist Performing arts *Albert Markov, Russian American violinist, composer *Alexa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Chains Prediction On N=3
Markov (Bulgarian, russian: Марков), Markova, and Markoff are common surnames used in Russia and Bulgaria. Notable people with the name include: Academics *Ivana Markova (born 1938), Czechoslovak-British emeritus professor of psychology at the University of Stirling * John Markoff (sociologist) (born 1942), American professor of sociology and history at the University of Pittsburgh *Konstantin Markov (1905–1980), Soviet geomorphologist and quaternary geologist Mathematics, science, and technology *Alexander V. Markov (1965-), Russian biologist *Andrey Markov (1856–1922), Russian mathematician *Vladimir Andreevich Markov (1871–1897), Russian mathematician, brother of Andrey Markov (Sr.) * Andrey Markov Jr. (1903–1979), Russian mathematician and son of Andrey Markov *John Markoff (born 1949), American journalist of computer industry and technology *Moisey Markov (1908–1994), Russian physicist Performing arts *Albert Markov, Russian American violinist, composer *Alexa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
