منابع مشابه
Fast Simulation Of New Coins From Old
Let S ⊂ (0, 1). Given a known function f : S → (0, 1), we consider the problem of using independent tosses of a coin with probability of heads p (where p ∈ S is unknown) to simulate a coin with probability of heads f(p). We prove that if S is a closed interval and f is real analytic on S, then f has a fast simulation on S (the number of p-coin tosses needed has exponential tails). Conversely, i...
متن کاملNew coins from old, smoothly
Given a (known) function f : [0, 1] → (0, 1), we consider the problem of simulating a coin with probability of heads f(p) by tossing a coin with unknown heads probability p, as well as a fair coin, N times each, where N may be random. The work of Keane and O’Brien (1994) implies that such a simulation scheme with IPp(N < ∞) = 1 exists iff f is continuous. Nacu and Peres (2005) proved that f is ...
متن کاملNew Coins From Old: Computing With Unknown Bias
Suppose that we are given a function f : (0, 1) → (0, 1) and, for some unknown p ∈ (0, 1), a sequence of independent tosses of a p-coin (i.e., a coin with probability p of “heads”). For which functions f is it possible to simulate an f(p)-coin? This question was raised by S. Asmussen and J. Propp. A simple simulation scheme for the constant function f(p) ≡ 1/2 was described by von Neumann (1951...
متن کاملSome old books and ancient coins from the Hunter Collection.
in the embarrassing situation of having little or no catgut industry. Some far-sighted Edinburgh surgeons, realizing the problems, requested a local pharmacist, George Merson to undertake the commercial manufacture of this material. This he did in an old manse at St. John's Hill in the Pleasance, Edinburgh, and by the end of the war the business was well under way. About this time Merson began ...
متن کاملNew Programs From Old
hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh There is often a need in the program-development process to generate a new version of a program that relates to existing versions of the program in some specific way. Program-development tools that assist in the generation of the new version, or possibly even automatically generate the new version from the e...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2005
ISSN: 1050-5164
DOI: 10.1214/105051604000000549