This paper is about the probability law of the integral of geometric Brownian motion over a finite time interval. A partial differential equation is derived for the Laplace transform of the law of the ...

Brownian motion – first explained by Albert Einstein in 1905 – describes the random, erratic motion of tiny particles dispersed in a fluid, collectively called a colloid. It is caused by the many ...

In this note we compute the Laplace transform of hitting times, to fixed levels, of integrated geometric Brownian motion. The transform is expressed in terms of the gamma and confluent hypergeometric ...

A second course in stochastic processes and applications to insurance. Markov chains (discrete and continuous time), processes with jumps; Brownian motion and diffusions; Martingales; stochastic ...

Foundational work on particle transport in asymmetrically modulated pores has further elucidated the role of geometric asymmetry in inducing directed motion under external bias [4].

Classical Brownian motion theory was established over one hundred year ago, describing the stochastic collision behaviors between surrounding molecules. Recently, researchers from Technical ...