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[4] [3] Medhi returned to Gauhati University where he became a professor and was the head of the department of statistics till he retired in 1985. [7] Earlier in Gauhati University, both mathematics and statistics were in a common department, however, under the able leadership of Prof Medhi, statistics became a full-fledged individual department.
In the theory of renewal processes, a part of the mathematical theory of probability, the residual time or the forward recurrence time is the time between any given time and the next epoch of the renewal process under consideration.
The process is Markovian only at the specified jump instants, justifying the name semi-Markov. [1] [2] [3] (See also: hidden semi-Markov model.) A semi-Markov process (defined in the above bullet point) in which all the holding times are exponentially distributed is called a continuous-time Markov chain. In other words, if the inter-arrival ...
In probability theory, a subordinator is a stochastic process that is non-negative and whose increments are stationary and independent. [1] Subordinators are a special class of Lévy process that play an important role in the theory of local time. [2]
The term stochastic process first appeared in English in a 1934 paper by Joseph Doob. [60] For the term and a specific mathematical definition, Doob cited another 1934 paper, where the term stochastischer Prozeß was used in German by Aleksandr Khinchin, [63] [64] though the German term had been used earlier, for example, by Andrei Kolmogorov ...
In the theory of stochastic processes in mathematics and statistics, the generated filtration or natural filtration associated to a stochastic process is a filtration associated to the process which records its "past behaviour" at each time. It is in a sense the simplest filtration available for studying the given process: all information ...
The objective of the stochastic scheduling problems can be regular objectives such as minimizing the total flowtime, the makespan, or the total tardiness cost of missing the due dates; or can be irregular objectives such as minimizing both earliness and tardiness costs of completing the jobs, or the total cost of scheduling tasks under likely arrival of a disastrous event such as a severe typhoon.
In probability theory, a stochastic process is said to have stationary increments if its change only depends on the time span of observation, but not on the time when the observation was started. Many large families of stochastic processes have stationary increments either by definition (e.g. Lévy processes) or by construction (e.g. random walks)