Biographical note: Mark Davis, Professor of Mathematics at Imperial College London, has written three books on stochastic modeling and control, most recently "Markov Models and Optimization". Alison Etheridge, Professor of Probability at the University of Oxford, is the author of "A Course in...

A process which we call symbiotic branching, is suggested covering three well-known interacting models: mutually catalytic branching, the stepping stone model, and the Anderson model. Basic tools such as self-duality, particle system moment duality, measure case moment duality, and moment...

The purposes of this paper are threefold: to suggest a conceptual scheme which encompasses innovations and improvements in industry; to express this scheme in the mathematical form of Poisson jump processes; and, finally, to illustrate it with a sequence of cost data drawn from three-quarters of...

March 29, 1900, is considered by many to be the day mathematical finance was born. On that day a French doctoral student, Louis Bachelier, successfully defended his thesis Théorie de la Spéculation at the Sorbonne. The jury, while noting that the topic was "far away from those usually...