TY  - INPR
A1  - Conforti, Giovanni
T1  - Reciprocal classes of continuous time Markov Chains
N2  - In this work we study reciprocal classes of Markov walks on graphs. Given a continuous time reference Markov chain on a graph, its reciprocal class is the set of all probability measures which can be represented as a mixture of the bridges of the reference walks. We characterize reciprocal classes with two different approaches. With the first approach we found it as the set of solutions to duality formulae on path space, where the differential operators have the interpretation of the addition of infinitesimal random loops to the paths of the canonical process. With the second approach we look at short time asymptotics of bridges. Both approaches allow an explicit computation  of reciprocal characteristics, which are divided into two families, the loop characteristics and the arc characteristics. They are those specific functionals of the generator of the reference chain which determine its reciprocal class. We look at the specific examples such as Cayley graphs, the hypercube and planar graphs. Finally we establish the first concentration of measure results for the bridges of a continuous time Markov chain based on the reciprocal characteristics.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 4 (2015) 8 
KW  - random walks on graphs
KW  - bridges of random walks
KW  - reciprocal characteristics
KW  - Schrödinger problem
KW  - integration by parts on path space
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-78234
SN  - 2193-6943
VL  - 4
IS  - 8
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  -