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The term strong Markov property is similar to the Markov property, except that the meaning of "present" is defined in terms of a random variable known as a stopping time. The term Markov assumption is used to describe a model where the Markov property is assumed to hold, such as a hidden Markov model .
Markov chains and continuous-time Markov processes are useful in chemistry when physical systems closely approximate the Markov property. For example, imagine a large number n of molecules in solution in state A, each of which can undergo a chemical reaction to state B with a certain average rate. Perhaps the molecule is an enzyme, and the ...
The chemical basis for Markovnikov's Rule is the formation of the most stable carbocation during the addition process. Adding the hydrogen ion to one carbon atom in the alkene creates a positive charge on the other carbon, forming a carbocation intermediate.
A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [12] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
Markov processes are stochastic processes, traditionally in discrete or continuous time, that have the Markov property, which means the next value of the Markov process depends on the current value, but it is conditionally independent of the previous values of the stochastic process. In other words, the behavior of the process in the future is ...
The simplest Markov model is the Markov chain.It models the state of a system with a random variable that changes through time. In this context, the Markov property indicates that the distribution for this variable depends only on the distribution of a previous state.
The strong Markov property is a generalization of the Markov property above in which t is replaced by a suitable random time τ : Ω → [0, +∞] known as a stopping time. So, for example, rather than "restarting" the process X at time t = 1, one could "restart" whenever X first reaches some specified point p of R n.
We say is Markov with initial distribution and rate matrix to mean: the trajectories of are almost surely right continuous, let be a modification of to have (everywhere) right-continuous trajectories, (()) = + almost surely (note to experts: this condition says is non-explosive), the state sequence (()) is a discrete-time Markov chain with ...