Bücher der Reihe Bocconi & Springer Series

We call peacock an integrable process which is increasing in the convex order;In this monograph, we exhibit numerous examples of peacocks and associated martingales with the help of different methods: construction of sheets, time reversal, time inversion, self-decomposability, SDE, Skorokhod embeddings.

The concept of Wiener chaos generalizes to an infinite-dimensional setting the properties of orthogonal polynomials associated with probability distributions on the real line.This book is concerned with combinatorial structures arising from the studyof chaotic random variables related to infinitely divisible random measures.

This book explores several aspects of fractional Brownian motion, including the stochastic integration, the study of its supremum and its appearance as limit of partial sums involving stationary sequences.

This research monograph provides an introduction to tractable multidimensional diffusion models. It also offers an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals.

Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics.

This book gives an overview of affine diffusions, from Ornstein-Uhlenbeck processes to Wishart processes and it considers some related diffusions such as Wright-Fisher processes. It focuses on different simulation schemes for these processes, especially second-order schemes for the weak error.

This book is devoted to parameter estimation in diffusion models involving fractional Brownian motion and related processes. In particular, models of financial markets demonstrate various kinds of memory and usually this memory is modeled by fractional Brownian diffusion.

Stochastic geometry is the branch of mathematics that studies geometric structures associated with random configurations, such as random graphs, tilings and mosaics.

The book constitutes an introduction to stochastic calculus, stochastic differential equations and related topics such as Malliavin calculus. On the other hand it focuses on the techniques of stochastic integration and calculus via regularization initiated by the authors. The definitions relies on a smoothing procedure  of the integrator process, they generalize the usual Ito and Stratonovich integrals for Brownian motion but the integrator could also not be a semimartingale and the integrand is allowed to be anticipating. The resulting calculus requires a simple formalism: nevertheless it entails pathwise techniques even though it takes into account randomness.  It allows connecting different types of pathwise and non pathwise integrals such as Young, fractional, Skorohod integrals, enlargement of filtration and rough paths. The covariation, but also high order variations, play a fundamental role in the calculus via regularization, which can also be applied for irregular integrators. A large class of Gaussian processes, various generalizations of semimartingales such that Dirichlet and weak Dirichlet processes are revisited. Stochastic calculus via regularization has been successfully used in applications, for instance in robust finance and on modeling vortex filaments in turbulence. The book is addressed to PhD students and researchers in stochastic analysis and applications to various fields.