Stochastic systems provide powerful abstract models for a variety of important real-life
applications: for example, power supply, traffic flow, data transmission. They (and the real …

Publisher Summary This chapter focuses on the random walk and fluctuation theory. The
theory and applications of random walks are ubiquitous in the modern probability literature …

Probability on groups gives a mathematical context to the interplay of chance with symmetry.
To study this subject involves investigating probability measures on groups and random …

A Particle Migrating Randomly on a Sphere Page 1 Journal of Theoretical Probability. Vol. 10.
No.2. 1997 A Particle Migrating Randomly on a Sphere David R. Brillinger1 Consider a particle …

Positive definite functions on metric spaces were considered by Schoenberg (26). We write
σk for the unit hypersphere in (k+ 1)-space; then σk is a metric space under geodesic …

It is a well-known fact that on the real line R and on the torus% there exists-up to isomorphy-
exactly one group operation which is compatible with the (usual) topology on these spaces …

Numerical simulations have been performed to determine the conduction heat transfer in a
sessile droplet for a large range of dynamic contact angle θ and Biot number B i. The …

This paper describes Gelfand pairs to statisticians and probabilists and deals with six typical
examples: euclidean space, sphere and cube; Poincaré half-plane, homogeneous tree and …

Let (S n∶ n>-1) be a random walk on a hypergroup (ℝ+,*), ie, a Markov chain with transition
kernel N (x, A)= ε x* μ (A), where μ is a fixed probability measure on ℝ+ such that the second …

Paul Lévy studied Gaussian processes ξ (a) with the parameter a running over Euclidean d-
space R d and he also studied the case when a runs over the d-sphere S d. His results were …