Levy and Solomon have found that random multiplicative processes wi =11 A2. At

We develop a completely new and straightforward method for simulating the joint law of the position and running maximum at a fixed time of a general Lévy process with a view to application in insurance and financial mathematics. Although different, our method takes lessons from Carr’s so-called “Canadization” technique as well as Doney’s method of stochastic bounds for Lévy processes; see Carr ...

We develop new representations for the Lévy measures of the beta and gamma processes. These representations are manifested in terms of an infinite sum of well-behaved (proper) beta and gamma distributions. Further, we demonstrate how these infinite sums may be truncated in practice, and explicitly characterize truncation errors. We also perform an analysis of the characteristics of posterior di...

We consider two stochastic processes, the Gribov process and the general epidemic process, that describe the spreading of an infectious disease. In contrast to the usually assumed case of short-range infections that lead, at the critical point, to directed and isotropic percolation respectively, we consider long-range infections with a probability distribution decaying in d dimensions with the ...

Lévy processes play an important role in the stochastic process theory. However, since samples are non-i.i.d., statistical learning results based on the i.i.d. scenarios cannot be utilized to study the risk bounds for Lévy processes. In this paper, we present risk bounds for non-i.i.d. samples drawn from Lévy processes in the PAC-learning framework. In particular, by using a concentration inequ...

Based on the theory of independently scattered random measures, we introduce a natural generalisation Gaussian space-time white noise to Levy-type setting, which call Levy-valued measures. We determine subclass cylindrical Levy processes correspond and describe elements this uniquely by their characteristic function. embed measure, or corresponding process, in space general tempered distributio...