What is stochastic processes?
Suppose that a real life process has been observed to have the characteristics of stochastic process.collection of random variable indexed by the parameter such as time and space are known as stockist process. So stochastic process have been used in real world phenomena.
Time series problem;
A behaviour study is aimed at understanding the general as well as specific detail of the behaviour of the system.one way to build an exact model and reduce the behaviour of the system from the model. the informations that can be derived from these model is limited by the complexities of the system and difficulties in their modifications.more efficient way would to be used the behavioral result derived from the analytical model in it another analytical model for the operational aspects of the system. A simple example would be that of minimising of cost equation for the system.
The gamblers ruin problems;
Gambler wins and lose dollar based on outcomes of a game this is depends on the probability. Let if the probability of a win and b is equal to 1 minus b the probability of loss.
Reliability problems;
the reliability of a system is defined as the probability that it is perform its assignment mission. If the mission is to accomplish a task with no reference to time we can consider it as a probability of success at a time .
Time sharing computer system;
Jobs of very dlink come to a computing centre from various sources.the number of jobs arriving as well as their length can be set to follow certain distribution.under these conditions the number of jobs waiting at any time and the time of job has to spend in the system can be represented by a stochastic process.
Population growth problems;
the external factor that influence the growth of animals such as weather conditions disease and availability of food are to very good and uncertain for deterministic model.when these factors are identified and accounted for the population size at any time can be considered a stochastic process.
Brand switching model for consumer behaviour;
Suppose there are three brands on the sales se capital A ,B and C..the consumer idhar by the same brand for few months for change their brand every now and then there is a also strong possibility that when a superior brand is introduced some of the old brand will be left with only a few consumers.
Recovery, Relapse and Death due to a Disease;
For instant four different states for the patients can be identified;
The initial state of being under treatment
The state of being dedh immediately following treatment
The state of recovery and
The state of being lost after recovery.
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