On extremal solutions of martingale problems
On harmonic functions of symmetric Lévy processes
We consider some classes of Lévy processes for which the estimate of Krylov and Safonov (as in (Potential Anal.17 (2002) 375–388)) fails and thus it is not possible to use the standard iteration technique to obtain a-priori Hölder continuity estimates of harmonic functions. Despite the failure of this method, we obtain some a-priori regularity estimates of harmonic functions for these processes. Moreover, we extend results from (Probab. Theory Related Fields135 (2006) 547–575) and obtain asymptotic...
On impulsive control with long run average cost criterion
On independent times and positions for Brownian motions.
On invariant measures of nonlinear Markov processes.
On jump processes with drift [Book]
On moments for branching processes
On optimal stopping of inhomogeneous standard Markov processes.
On recurrent and transient sets of inhomogeneous symmetric random walks.
On sequentially weakly Feller solutions to SPDE’s
A rather general class of stochastic evolution equations in Hilbert spaces whose transition semigroups are Feller with respect to the weak topology is found, and consequences for existence of invariant measures are discussed.
On small stochastic perturbations of mappings of the unit interval
On subordinators, self-similar Markov processes and some factorizations of the exponential variable.
On the asymptotic behaviour of increasing self-similar Markov processes.
On the control of the difference between two Brownian motions: a dynamic copula approach
We propose new copulae to model the dependence between two Brownian motions and to control the distribution of their difference. Our approach is based on the copula between the Brownian motion and its reflection. We show that the class of admissible copulae for the Brownian motions are not limited to the class of Gaussian copulae and that it also contains asymmetric copulae. These copulae allow for the survival function of the difference between two Brownian motions to have higher value in the right...
On the control of the difference between two Brownian motions: an application to energy markets modeling
We derive a model based on the structure of dependence between a Brownian motion and its reflection according to a barrier. The structure of dependence presents two states of correlation: one of comonotonicity with a positive correlation and one of countermonotonicity with a negative correlation. This model of dependence between two Brownian motions B1 and B2 allows for the value of [...] to be higher than 1/2 when x is close to 0, which is not the case when the dependence is modeled by a constant...
On the coupling property of Lévy processes
We give necessary and sufficient conditions guaranteeing that the coupling for Lévy processes (with non-degenerate jump part) is successful. Our method relies on explicit formulae for the transition semigroup of a compound Poisson process and earlier results by Mineka and Lindvall–Rogers on couplings of random walks. In particular, we obtain that a Lévy process admits a successful coupling, if it is a strong Feller process or if the Lévy (jump) measure has an absolutely continuous component.
On the equivalence of some eternal additive coalescents
In this paper, we study additive coalescents. Using their representation as fragmentation processes, we prove that the law of a large class of eternal additive coalescents is absolutely continuous with respect to the law of the standard additive coalescent on any bounded time interval.
On the first-passage time of integrated Brownian motion.
On the Ray topology
On the reconstruction of a killed Markov process