Davis-type inequalities for a number of diffusion processes.
Decoherence of quantum Markov semigroups
Décomposition du mouvement brownien avec dérive en un minimum local par juxtaposition de ses excursions positives et négatives
Decompositional analysis of Kronecker structured Markov chains.
Degenerate stochastic differential equations arising from catalytic branching networks.
Degenerate stochastic differential equations for catalytic branching networks
Uniqueness of the martingale problem corresponding to a degenerate SDE which models catalytic branching networks is proven. This work is an extension of the paper by Dawson and Perkins [Illinois J. Math.50 (2006) 323–383] to arbitrary catalytic branching networks. As part of the proof estimates on the corresponding semigroup are found in terms of weighted Hölder norms for arbitrary networks, which are proven to be equivalent to the semigroup norm for this generalized setting.
Démonstration d'un théorème de F. Knight à l'aide de martingales exponentielles
Démonstration probabiliste du théorème de d'Alembert
Démonstration probabiliste d'une identité de convolution
Densité des diffusions en temps petit : développements asymptotiques (part I)
Densité des orbites des trajectoires browniennes sous l’action de la transformation de Lévy
Let Tbe a measurable transformation of a probability space , preserving the measureπ. Let X be a random variable with law π. Call K(⋅, ⋅) a regular version of the conditional law of X given T(X). Fix . We first prove that ifB is reachable from π-almost every point for a Markov chain of kernel K, then the T-orbit of π-almost every point X visits B. We then apply this result to the Lévy transform, which transforms the Brownian motion W into the Brownian motion |W| − L, where L is the local time...
Densité en temps petit d'un processus de saut
Density in small time for Levy processes
Density in small time for Lévy processes
The density of real-valued Lévy processes is studied in small time under the assumption that the process has many small jumps. We prove that the real line can be divided into three subsets on which the density is smaller and smaller: the set of points that the process can reach with a finite number of jumps (Δ-accessible points); the set of points that the process can reach with an infinite number of jumps (asymptotically Δ-accessible points); and the set of points that the process cannot...
Density of paths of iterated Lévy transforms of brownian motion
The Lévy transform of a Brownian motion B is the Brownian motion B(1) given by Bt(1) = ∫0tsgn(Bs)dBs; call B(n) the Brownian motion obtained from B by iterating n times this transformation. We establish that almost surely, the sequence of paths (t → Bt(n))n⩾0 is dense in Wiener space, for the topology of uniform convergence on compact time intervals.
Density of paths of iterated Lévy transforms of Brownian motion
The Lévy transform of a Brownian motion B is the Brownian motion B(1) given by Bt(1) = ∫0tsgn(Bs)dBs; call B(n) the Brownian motion obtained from B by iterating n times this transformation. We establish that almost surely, the sequence of paths (t → Bt(n))n⩾0 is dense in Wiener space, for the topology of uniform convergence on compact time intervals.
Dependent defaults and credit migrations
The paper deals with the modelling of mutually dependent default times of several credit names through the intensity-based approach. We extend to the case of multiple ratings some previous results due to Schmidt (1998), Kusuoka (1999) and Jarrow and Yu (2001). The issue of the arbitrage valuation of simple basket credit derivatives is also briefly examined. We argue that our approach leads, in some cases, to a significant reduction of the dimensionality of the valuation problem at hand.
Derivation of the tumour control probability (TCP) from a cell cycle model.
Dérivation par rapport au processus de Bessel
Description de certains processus markoviens indexés par des sous-ensembles du cercle