Markovian bridges and reversible diffusions with jumps
| Nicolas Privault |
|
Jean-Claude Zambrini |
| Département de Mathématiques |
|
Grupo de Física Matemática |
| Université de la Rochelle |
|
Universidade de Lisboa |
| 17042 La Rochelle Cedex 1 |
|
16049-003 Lisboa |
| France |
|
Portugal |
Abstract:
Markovian bridges driven by Lévy processes are constructed
from the data of an initial and a final distribution,
as particular cases of a family of time
reversible diffusions with jumps.
The processes obtained in this way are essentially the only
(not necessarily continuous) Markovian Bernstein processes.
These processes are also characterized using the theory of
stochastic control for jump processes.
Our construction is motivated by
Euclidean quantum mechanics in momentum representation,
but the resulting class of processes is much
bigger than the one needed for this purpose.
A large collection of examples is included.
Key words: Lévy processes,
bridges, time reversal, Euclidean quantum mechanics.
Mathematics Subject Classification (1991):
60J25, 81S20, 47D07.
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