Summary In many cases, a Markov chain exhibits a long-term limiting behavior. The chain settles down to an equilibrium distribution, which is independent of its initial state. The long-term behavior of a Markov chain is related to how often states are visited. This chapter addresses the ...
Long-Term Frequency Interpretations 从频率学的角度来说,当试验次数 n 很大的时候,事件发生的频率同样可以表示事件发生的概率,那么 \pi_j=\lim_{n \rightarrow \infty}{\frac{v_{ij}(n)}{n}}, v_{ij}(n) 状态i 转移到到 j 的总次数。 记q_{kj}(n) 是状态 k\rightarrow j 的次数,那么有 ...
[Section 1] DISCRETE-TIME MARKOV CHAINS(系统每一步的状态可能不同)(系统的下一个状态只和当前状态有关) The state changes at certain discrete time instants, indexed by an integer variable n . State space(每一步的状态可能不同) At each time step n , the state of the chain is denoted by ...
In this section, we review Markov chains and discuss some key results. 9.1.1 Overview A Markov chain is a model of the random motion of an object in a discrete set of possible locations. Two versions of this model are of interest to us: discrete time and continuous time. In discrete ti...
Markov Chains are a powerful tool in probability theory and statistics. They represent a sequence of random events where the probability of an event depends only on the outcome of the previous event. The chain consists of a set of states and a set of transition probabilities between states. Ma...
This means in the long term we areequallyas likely to be in any of the three states! Note: This wasn’t a dense deep derivation of the stationary distribution as I didn’t want it turn into a textbook! However, there are many in-depth examples online abouteigenvalue decomposition. ...
不过,对于 periodic Markov chain,其稳态分布不再表示 Markov chain 在无穷多步后处于状态 i 的极限概率,而只对应访问状态 i 的long-term frequency. 任意的 finite Markov chain 中都存在一个 recurrent 的 communicating class,其对应的 subchain 就会是 irreducible 并且 recurrent 的,如果其还是 aperiodic 的,...
A continuous-time Markov chain is time reversible if the process in forward time is indistinguishable from the process in reversed time. A consequence is that for all states i and j, the long-term forward transition rate from i to j is equal to the long-term backward rate from j to i....
Markov_Chain Formally, a Markov chain is a discrete (discrete-time) random process with the Markov property. Often, the term "Markov chain" is used to mean a Markov process which has a discrete (finite or countable) state-space. Usually a Markov chain would be defined for a discrete set ...
404 MARKOV CHAINSSynergy between these two approaches to marine conservation and management arises from use of marine reserves as tools in the marine ecosystem–based manage-ment portfolio. Within reserves and reserve networks, conservation objectives may be achieved as resident target species and ...