The random walk theorem, first presented by French mathematician Louis Bachelier in 1900 and then expanded upon by economist Burton Malkiel in his 1973 book A Random Walk Down Wall Street, asserts ...

We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk ...

Theory that stock price changes from day to day are accidental or haphazard; changes are independent of each other and have the same probability distribution. For a simple random walk, the best ...

Journal of Applied Probability, Vol. 36, No. 1 (Mar., 1999), pp. 78-85 (8 pages) This paper is concerned with submultiplicative moments for the stationary distributions π of some Markov chains taking ...

Explain why probability is important to statistics and data science. See the relationship between conditional and independent events in a statistical experiment. Calculate the expectation and variance ...

Mathematicians from the California Institute of Technology have solved an old problem related to a mathematical process called a random walk. The team, which also worked with a colleague from Israel’s ...