A newly discovered set of mathematical equations describes how to turn any sequence of random events into a clock, scientists ...

Random walks constitute a foundational concept in probability theory, describing the seemingly erratic movement of particles or agents as they traverse a space in a series of stochastic steps. In many ...

Branching processes in random environments constitute a significant class of stochastic models designed to capture the interplay between intrinsic reproductive dynamics and extrinsic environmental ...

Tiny particles like pollen grains move constantly, pushed and pulled by environmental forces. To study this motion, physicists use a "random walk" model—a system in which every step is determined by a ...

Journal of the Royal Statistical Society. Series A (General), Vol. 147, No. 2, The 150th Anniversary of the Royal Statistical Society (1984), pp. 233-244 (12 pages) Probability theory as a branch of ...

This paper is concerned with everywhere local behaviour of certain classes of random processes which have stationary Gaussian increments. It is shown that for two classes of processes almost all the ...

Silicon photonics is rapidly emerging as a promising technology to enable higher bandwidth, lower energy, and lower latency communication and information processing, and other applications. In silicon ...