TY  - INPR
A1  - Cattiaux, Patrick
A1  - Dai Pra, Paolo
A1  - Poelly, Sylvie
T1  - A constructive approach to a class of ergodic HJB equations with nonsmooth cost
N2  - We consider a class of ergodic Hamilton-Jacobi-Bellman (HJB) equations, related to large time asymptotics of non-smooth multiplicative functional of difusion processes. Under suitable ergodicity assumptions on the underlying difusion, we show existence of these asymptotics, and that they solve the related HJB equation in the viscosity sense.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2007, 02 
Y1  - 2007
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-49430
ER  - 
TY  - GEN
A1  - Roelly, Sylvie
A1  - Dai Pra, Paolo
T1  - An existence result for infinite-dimensional Brownian diffusions with non- regular and non Markovian drift
N2  - We prove in this paper an existence result for infinite-dimensional stationary interactive Brownian diffusions. The interaction is supposed to be small in the norm ||.||∞ but otherwise is very general, being possibly non-regular and non-Markovian. Our method consists in using the characterization of such diffusions as space-time Gibbs fields so that we construct them by space-time cluster expansions in the small coupling parameter.
KW  - infinite-dimensional Brownian diffusion
KW  - space-time Gibbs field
KW  - cluster expansion
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6684
ER  - 
TY  - JOUR
A1  - Dai Pra, Paolo
A1  - Louis, Pierre-Yves
A1  - Minelli, Ida
T1  - Monotonicity and complete monotonicity for continuous-time Markov chains
N2  - We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in continuous time but not in discrete-time
Y1  - 2006
UR  - http://www.elsevier.com/locate/issn/1631073X
U6  - https://doi.org/10.1016/j.crma.2006.04.007
SN  - 1631-073X
ER  - 
TY  - GEN
A1  - Dai Pra, Paolo
A1  - Louis, Pierre-Yves
A1  - Minelli, Ida
T1  - Monotonicity and complete monotonicity for continuous-time Markov chains
N2  - We analyze the notions of monotonicity and complete monotonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which monotonicity and complete monotonicity coincide in continuous time but not in discrete-time.
N2  - Nous étudions les notions de monotonie et de monotonie complète pour les processus de Markov (ou chaînes de Markov à temps continu) prenant leurs valeurs dans un espace partiellement ordonné. Ces deux notions ne sont pas équivalentes, comme c'est le cas lorsque le temps est discret. Cependant, nous établissons que pour certains ensembles partiellement ordonnés, l'équivalence a lieu en temps continu bien que n'étant pas vraie en temps discret.
KW  - Stochastik
KW  - continuous time Markov Chains
KW  - poset
KW  - monotonicity
KW  - coupling
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-7665
ER  - 
TY  - INPR
A1  - Conforti, Giovanni
A1  - Dai Pra, Paolo
A1  - Roelly, Sylvie
T1  - Reciprocal class of jump processes
N2  - Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of compound Poisson processes whose jumps belong to a finite set A in R^d. We propose a characterization of the reciprocal class as the unique set of probability measures on which a family of time and space transformations induces the same density, expressed in terms of the reciprocal invariants. The geometry of A plays a crucial role in the design of the transformations, and we use tools from discrete geometry to obtain an optimal characterization. We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 3 (2014) 6 
KW  - reciprocal processes
KW  - stochastic bridges
KW  - jump processes
KW  - compound Poisson processes
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-70776
SN  - 2193-6943
VL  - 3
IS  - 6
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  -