Lévy processes form a wide and rich class of random process, and have many applications
ranging from physics to finance. Stochastic calculus is the mathematics of systems …

This volume concentrates on how to construct a Markov process by starting with a suitable
pseudo-differential operator. Feller processes, Hunt processes associated with Lp-sub …

This volume concentrates on how to construct a Markov process by starting with a suitable
pseudo-differential operator. Feller processes, Hunt processes associated with Lp-sub …

Let (A, D (A)) be the infinitesimal generator of a Feller semigroup such that C c∞(ℝ n)⊂ D
(A) and A| C c∞(ℝ n) is a pseudo-differential operator with symbol− p (x, ξ) satisfying| p (• …

Our aim in this survey is to show how pseudodifferential operators arise naturally in the
theory of Markov processes and that this opens the way to use Fourier analytic techniques …

We prove the superposition principle for probability measure-valued solutions to non-local
Fokker–Planck–Kolmogorov equations, which in turn yields the equivalence between …

In this paper we study a family of nonlinear (conditional) expectations that can be
understood as a diffusion with uncertain local characteristics. Here, the differential …

We consider stochastic differential equations which are driven by multidimensional Levy
processes. We show that the infinitesimal generator of the solution is a pseudo-differential …

This paper develops a spectral theory of Markovian asset pricing models where the
underlying economic uncertainty follows a continuous-time Markov process X with a general …

We derive explicitly the coupling property for the transition semigroup of a Lévy process and
gradient estimates for the associated semigroup of transition operators. This is based on the …