Stochastic differential equations (SDEs) and random processes form a central framework for modelling systems influenced by inherent uncertainties. These mathematical constructs are used to rigorously ...

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 ...

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 ...

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 ...

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 ...

We describe a new class of self-similar symmetric α-stable processes with stationary increments arising as a large time scale limit in a situation where many users are earning random rewards or ...

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 ...

Random processes take place all around us. It rains one day but not the next; stocks and bonds gain and lose value; traffic jams coalesce and disappear. Because they’re governed by numerous factors ...

Silicon photonics uses existing CMOS manufacturing infrastructure and techniques but lacks mature models that take into account known CMOS process variations and their effect on photonic component ...