Notes on stochastic approximation methods
نویسندگان
چکیده
منابع مشابه
On Stochastic Approximation Methods in Reliability
Depending on the state of the stand-by equipment, can be distinguished loaded, non-loaded and partially loaded relief. In the case of loaded relief, the stand-by unit is in the same state as the operating unit and for this reason has the same intensity of breakdowns. In the partially loaded case, the stand-by device is loaded, but not so fully as the main equipment and for this reason has a dif...
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i=1 pi ≤ max 1≤i≤n pi, (6.1) where λ := EW = ∑n i=1 pi. Clearly, if the pi’s are not all small, there may be little content in (6.1). This is to be expected, since then EW = λ and VarW = λ − ∑n i=1 p 2 i need no longer be close to one another, whereas Poisson distributions have equal mean and variance. This makes it more natural to try to find a family of distributions for the approximation wit...
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(ii) F is a family of subsets of Ω which has the structure of a σ-field: a) ∅ ∈ F b) If A ∈ F , then its complement A also belongs to F c) A1, A2, . . . ∈ F =⇒ ∪i=1Ai ∈ F (iii) P is a function which associates a number P (A) to each set A ∈ F with the following properties: a) 0 ≤ P (A) ≤ 1, b) P (Ω) = 1 c) For any sequence A1, A2, . . . of disjoints sets in F (that is, Ai∩Aj = ∅ if i 6= j), P (...
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A stochastic process is a type of mathematical object studied in mathematics, particularly in probability theory, which can be used to represent some type of random evolution or change of a system. There are many types of stochastic processes with applications in various fields outside of mathematics, including the physical sciences, social sciences, finance and economics as well as engineering...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1958
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1958.100283