İŞLETME KARAR MODELLERİ

If the state space S of a stochastic process is discrete, the process is called discrete-state process often referred as a chain.

Familiar examples of stochastic processes are as follows:
• daily prices of a stock or exchange rate fluctuations,
• failures times of a machine,
• medical data such as a patient’s blood pressure or EKG,
• radar measurements for the position of an airplane,
• tossing a coin.

"Minting a coin" is not an example of a stochastic process.

The most common dependence structure is called Markov Property.

The probabilities of going from one state to another are called transition probabilities.

The n-step transition probability pij(n) is the probability that a process in state j will be in state i after n additional transitions.

A transition matrix is called regular if some power of the matrix includes all positive entries.

A state is called periodic, if it can only return to itself after a fixed number of transitions greater than 1.

They are used to analyse different decision situations.

It is a family of random variables.

If the state space S of a stochastic process finite, or countable, then the process is called a chain.

The most common dependence structure is called Markov Property.

The probabilities of going from one state to another are called transition probabilities.

A transition matrix is called regular if some power of the matrix includes all positive entries.

A state with a self-loop transition is always aperiodic.

State i is recurrent if, upon entering state i, the system will definitely return to state i. If a state is not recurrent, it is transient.

The main goal of a Markov chain is to calculate the probability that a system occupies a given state Si , when n is very large. This probability is called the limiting probability and it may converge to steady-state values that are independent of the initial state.

A stochastic process is a mathematical model that develops over time in a probabilistic manner.