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In probability theory and statistics, a stochastic order quantifies the concept of one random variable being "bigger" than another. These are usually partial orders , so that one random variable A {\displaystyle A} may be neither stochastically greater than, less than, nor equal to another random variable B {\displaystyle B} .
Stochastic dominance is a partial order between random variables. [1] [2] It is a form of stochastic ordering.The concept arises in decision theory and decision analysis in situations where one gamble (a probability distribution over possible outcomes, also known as prospects) can be ranked as superior to another gamble for a broad class of decision-makers.
Stochastic optimization also accounts for demand volatility which is a top priority among the challenges faced by supply chain professionals. [14] For example, management predicts a 65 percent probability of selling 500 units, a 20 percent probability of selling 400 units and a 15 percent probability of selling 600 units.
The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that certain properties of a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied. The ...
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 ...
If a stochastic process is strict-sense stationary and has finite second moments, it is wide-sense stationary. [2]: p. 299 If two stochastic processes are jointly (M + N)-th-order stationary, this does not guarantee that the individual processes are M-th- respectively N-th-order stationary. [1]: p. 159
A stochastic process has the Markov property if the conditional probability distribution of future states of the process (conditional on both past and present values) depends only upon the present state; that is, given the present, the future does not depend on the past.
In (), the first order loss function [(,)] captures the expected shortage quantity; its complement, [(,)], denotes the expected product quantity in stock at the end of the period. [ 10 ] On the basis of this cost function the determination of the optimal inventory level is a minimization problem.