To analyze whether stock-market prices follow a random walk, the algebraic sign of their returns has been compared with a coin toss, which is a prominent example for a Bernoulli trial with equiprobable outcomes. Like coin tosses, signed returns lend themselves for a simple runs test for...

To analyze whether stock-market prices follow a random walk, the algebraic sign of their returns has been compared with a coin toss, which is a prominent example for a Bernoulli trial with equiprobable outcomes. Like coin tosses, signed returns lend themselves for a simple runs test for...

Consider two independent random walks. By chance, there will be spells of association between them where the two processes move in the same direction, or in opposite direction. We compute the probabilities of the length of the longest spell of such random association for a given sample size, and...

A biased coin is tossed n times independently and sequentially. A “head” switch is a tail followed by a head and a “tail” switch is a head followed by a tail. Joint Laplace transforms for the number of “head” switches and “tail” switches are given. For the total number of...

We consider the optimization problem of a decision maker facing a sequence of coin tosses with an initially unknown probability Θ for heads. Before each toss she bets on either heads or tails and she wins one euro if she guesses correctly, otherwise she loses one euro. We investigate the effect...

We consider the optimization problem of a decision maker facing a sequence of coin tosses with an initially unknown probability Θ for heads. Before each toss she bets on either heads or tails and she wins one euro if she guesses correctly, otherwise she loses one euro. We investigate the effect...

We give a characterization of how fast the block length k may grow in order to have the relative frequence of occurrences of Blocks of length k among the first n tosses of a fair coin be 'good' approximations of their probabilities. The borderline will roughly be the logarithm of n with base 2,...