The purpose of this review article is to give an up to date account of the theory and
applications of scale functions for spectrally negative Lévy processes. Our review also …

Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …

Mathematical finance has grown into a huge area of research which requires a lot of care
and a large number of sophisticated mathematical tools. The subject draws upon quite …

Lévy processes are the natural continuous-time analogue of random walks and form a rich
class of stochastic processes around which a robust mathematical theory exists. Their …

This paper studies the first passage times to flat boundaries for a double exponential jump
diffusion process, which consists of a continuous part driven by a Brownian motion and a …

This is a survey article about occupation densities for both random and nonrandom vector
fields X:T→R^d where T⊂R^N. For N=d=1 this has previously been called the" local time" of …

The main goal of this work is to investigate the genealogical structure of continuousstate
branching processes in connection with limit theorems for discrete Galton-Watson trees …

Foreword 1. Elements on subordinators 1.1. Definitions and first properties 1.2. The Lévy-
Khintchine formula 1.3. The renewal measure 1.4. The range of a subordinator 2 …

This book begins with a historical survey ofgeneralized inverse Gaussian laws', in which the
wartime contribution of Etienne Halphen is presented for the first time. The inverse Gaussian …

Consider the American put and Russian option (Ann. Appl. Probab. 3 (1993) 603; Theory
Probab. Appl. 39 (1994) 103; Ann. Appl. Probab. 3 (1993) 641) with the stock price modeled …