5 citations · 20 across the 10 of their papers we have counts for
11 papers
Infinite-variation Lévy processes are either strongly eroded or abrupt
Jorge González Cázares, David Kramer-Bang, Aleksandar Mijatović
We prove that every real Lévy process of infinite variation is either abrupt or strongly eroded, resolving the conjectured geometric dichotomy on the smoothness of the convex hull…
Fast exact simulation of the first-passage event of a subordinator
Jorge Ignacio González Cázares, Feng Lin, Aleksandar Mijatović
This paper provides an exact simulation algorithm for the sampling from the joint law of the first-passage time, the undershoot and the overshoot of a subordinator crossing a non-i…
Brownian motion with asymptotically normal reflection in unbounded domains: from transience to stability
Miha Brešar, Aleksandar Mijatović, Andrew Wade
We quantify the asymptotic behaviour of multidimensional drifltess diffusions in domains unbounded in a single direction, with asymptotically normal reflections from the boundary.…
Fast exact simulation of the first passage of a tempered stable subordinator across a non-increasing function
Jorge Ignacio González Cázares, Feng Lin, Aleksandar Mijatović
We construct a fast exact algorithm for the simulation of the first-passage time, jointly with the undershoot and overshoot, of a tempered stable subordinator over an arbitrary non…
Optimal Markovian coupling for finite activity Lévy processes
Wilfrid S. Kendall, Mateusz B. Majka, Aleksandar Mijatović
We study optimal Markovian couplings of Markov processes, where the optimality is understood in terms of minimization of concave transport costs between the time-marginal distribut…
How smooth can the convex hull of a Lévy path be?
David Bang, Jorge González Cázares, Aleksandar Mijatović
We describe the rate of growth of the derivative of the convex minorant of a Lévy path at times where increases continuously. Since the convex minorant is piecewise linea…
Hölder continuity of the convex minorant of a Lévy process
Jorge González Cázares, David Kramer-Bang, Aleksandar Mijatović
We characterise the Hölder continuity of the convex minorant of most Lévy processes. The proof is based on a novel connection between the path properties of the Lévy process at zer…
When is the convex hull of a Lévy path smooth?
David Bang, Jorge Ignacio González Cázares, Aleksandar Mijatović
We characterise, in terms of their transition laws, the class of one-dimensional Lévy processes whose graph has a continuously differentiable (planar) convex hull. We show that thi…
Reflecting Brownian motion in generalized parabolic domains: explosion and superdiffusivity
Mikhail V. Menshikov, Aleksandar Mijatović, Andrew R. Wade
For a multidimensional driftless diffusion in an unbounded, smooth, sub-linear generalized parabolic domain, with oblique reflection from the boundary, we give natural conditions u…
Asymptotic shape of the concave majorant of a Lévy process
David Bang, Jorge Ignacio González Cázares, Aleksandar Mijatović
We establish distributional limit theorems for the shape statistics of a concave majorant (i.e. the fluctuations of its length, its supremum, the time it is attained and its value…
Monte Carlo algorithm for the extrema of tempered stable processes
Jorge Ignacio González Cázares, Aleksandar Mijatović
We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained and the position at a given (constant) time of an exp…