Absolute continuity of Markov processes
Bivariate Revuz measures and the Feynman-Kac formula
Comparaison des exposants de Lyapounov des processus markoviens multiplicatifs
Erratum / Correction to : “Minimization of the Kullback information of diffusion processes”
Exponential stability for nonlinear filtering
Fonctionnelles multiplicatives et sous-processus des P-processus
Girsanov and Feynman–Kac type transformations for symmetric Markov processes
Kac functional and Schrödinger equation
Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX
We obtain a local limit theorem for the laws of a class of Brownian additive functionals and we apply this result to a penalisation problem. We study precisely the case of the additive functional: . On the other hand, we describe Feynman-Kac type penalisation results for long Brownian bridges thus completing some similar previous study for standard Brownian motion (see [B. Roynette, P. Vallois and M. Yor, Studia Sci. Math. Hung.43 (2006) 171–246]).
Minimization of the Kullback information of diffusion processes
Multiplicative functionals and the stable topology
Multiplicative functionals of dual processes
Let and be a pair of dual standard Markov processes. We associate to each exact multiplicative function , of a unique exact , of in a natural manner. Any , is assumed to satisfy . The map is bijective and multiplicative in the sense that: .This correspondence is studied in some detail and several important examples are discussed.These results are then applied to study additive functionals.
On the stability of nonlinear Feynman-Kac semigroups
Renewal series and square-root boundaries for Bessel processes.
Some consequences of the cyclic exchangeability property for exponential functionals of Lévy processes
Time-dependent Schrödinger perturbations of transition densities
We construct the fundamental solution of for functions q with a certain integral space-time relative smallness, in particular for those satisfying a relative Kato condition. The resulting transition density is comparable to the Gaussian kernel in finite time, and it is even asymptotically equal to the Gaussian kernel (in small time) under the relative Kato condition. The result is generalized to arbitrary strictly positive and finite time-nonhomogeneous transition densities on measure spaces. We...