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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 ...
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 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]
In numerical methods for stochastic differential equations, the Markov chain approximation method (MCAM) belongs to the several numerical (schemes) approaches used in stochastic control theory. Regrettably the simple adaptation of the deterministic schemes for matching up to stochastic models such as the Runge–Kutta method does not work at all.
A real-valued stochastic process X is a submartingale if and only if it has a Doob decomposition into a martingale M and an integrable predictable process A that is almost surely increasing. [5] It is a supermartingale, if and only if A is almost surely decreasing.
In probability theory, a piecewise-deterministic Markov process (PDMP) is a process whose behaviour is governed by random jumps at points in time, but whose evolution is deterministically governed by an ordinary differential equation between those times.