In probability theory, an event is said to happen almost surely (sometimes abbreviated as a.s.) if it happens with probability 1 (with respect to the...
10 KB (1,425 words) - 05:45, 23 September 2024
Convergence of random variables (redirect from Almost sure convergence)
converges almost completely, or almost in probability towards X. When Xn converges almost completely towards X then it also converges almost surely to X....
41 KB (5,280 words) - 21:51, 25 September 2024
Infinite monkey theorem (section Almost surely)
time will almost surely type any given text, including the complete works of William Shakespeare. In fact, the monkey would almost surely type every...
50 KB (6,674 words) - 15:09, 7 September 2024
{\mathcal {F}}} is called almost surely invariant if and only if its indicator function 1 S {\displaystyle 1_{S}} is almost surely equal to the indicator...
10 KB (1,461 words) - 11:53, 27 July 2024
Proofs of convergence of random variables (section Convergence almost surely implies convergence in probability)
{ X n } {\displaystyle \{X_{n}\}} converges to X {\displaystyle X} almost surely, it means that the set of points O = { ω ∣ lim X n ( ω ) ≠ X ( ω ) }...
14 KB (2,462 words) - 18:01, 16 September 2024
Almost periodic function - and Operators Almost all Almost surely Approximation List of mathematical jargon "Almost All Real Numbers are Transcendental -...
2 KB (250 words) - 06:01, 4 March 2024
complement is of measure zero. In probability theory, the terms almost surely, almost certain and almost always refer to events with probability 1 not necessarily...
9 KB (1,261 words) - 12:11, 1 July 2024
{\mathcal {N}}(0,u).} W {\displaystyle W} has almost surely continuous paths: W t {\displaystyle W_{t}} is almost surely continuous in t {\displaystyle t} . That...
35 KB (5,899 words) - 10:47, 1 October 2024
flips will almost surely converge to 1⁄2 as n approaches infinity. Although the proportion of heads (and tails) approaches 1⁄2, almost surely the absolute...
45 KB (6,300 words) - 06:21, 26 September 2024
\alpha }} has almost surely pure point spectrum and exhibits Anderson localization. (It is known that almost surely can not be replaced by surely.) That the...
10 KB (1,325 words) - 18:04, 19 May 2024