… models, are used to approximate one dimensional diffusions, … focus on Lévy flights, stable
pure jump Lévy processes, which … stationary increments are distributed according to a Lévy …

… We also find that failure of the Feller condition can usually be … process, which does not
have independent increments. Hence, the time changed pure jump Lévy process is not Markov …

… increment infinitely divisible processes; this class includes many infinitely divisible processes
of interest, including linear fractional processes, … processes driven by Lévy processes. …

… for processes whose marginal distributions have Lévy -… diffusion We consider the U-valued
Feller diffusion (Ut)t≥0 the process … Recall that in the approximating individual based model …

… nonmonotone paths that has stationary independent increments and, under P0, almost …
Feller processes (see especially [3, Theorem 4.2]), and to [13] in the context of Lévy processes (…

… process; stochastic differential equations, Markov chain, … This gives, in most cases, different
distributions for Levy’s … on the objective: exact or approximated, with a fixed total length or not…

… possibility to numerically approximate semistable densities. … 3, we finally introduce Feller
semigroups and their generators… if A(0) = 0 almost surely, the increments are independent and …

… the practical motivation, consider the prototype weak convergence result : approximating …
processes with independent increments are sus of Erownian motion and Poisson processes, it …

… process with independent and stationary increments \(g_s^{-1}g_t\) for s ≤ t. Equivalently,
a Lévy process … The transition semigroup P t of g t is a left invariant and conservative Feller …

… theory of inhomogeneous Lévy processes in the homogeneous spaces … For general σ and
τ, we may approximate them by … By (2.10), the generator of x t as a Feller process in X = Y × Z …