This paper introduces the class of volatility modulated Lévy-driven Volterra (VMLV)
processes and their important subclass of Lévy semistationary (LSS) processes as a new …

Ambit Stochastics has emerged as a new field in probability theory during the last decade.
While there are still many open questions and challenges, we think that the time is right to …

A new class of stochastic processes, termed Brownian semistationary processes (BSS), is
introduced and discussed. This class has similarities to that of Brownian semimartingales …

We obtain general weak existence and stability results for stochastic convolution equations
with jumps under mild regularity assumptions, allowing for non-Lipschitz coefficients and …

Fractional processes have gained popularity in financial modeling due to the dependence
structure of their increments and the roughness of their sample paths. The non-Markovianity …

The question of existence and properties of stationary solutions to Langevin equations
driven by noise processes with stationary increments is discussed, with particular focus on …

Various characterizations for fractional Lévy processes to be of finite variation are obtained,
one of which is in terms of the characteristic triplet of the driving Lévy process, while others …

We define two new classes of stochastic processes, called tempered fractional Lévy process
of the first and second kinds (TFLP and TFLP II, respectively). TFLP and TFLP II make up …

Stationary infinitely divisible processes Page 1 Brazilian Journal of Probability and Statistics
2011, Vol. 25, No. 3, 294–322 DOI: 10.1214/11-BJPS140 © Brazilian Statistical Association …

In this paper we present a survey on recent developments in the study of ambit fields and
point out some open problems. Ambit fields is a class of spatio-temporal stochastic …