TY - JOUR
T1 - A duality relation for entrance and exit laws for Markov processes
AU - Cox, J. Theodore
AU - Rösler, Uwe
N1 - Funding Information:
by NSF grant MC’S
PY - 1984/2
Y1 - 1984/2
N2 - Markov processes Xt on (X, FX) and Yt on (Y, FY) are said to be dual with respect to the function f(x, y) if Exf(Xt, y) = Eyf(x, Yt for all x ε{lunate} X, y ε{lunate} Y, t ≥ 0. It is shown that this duality reverses the role of entrance and exit laws for the processes, and that two previously published results of the authors are dual in precisely this sense. The duality relation for the function f(x, y) = 1{x is established for one-dimensional diffusions, and several new results on entrance and exit laws for diffusions, birth-death processes, and discrete time birth-death chains are obtained.
AB - Markov processes Xt on (X, FX) and Yt on (Y, FY) are said to be dual with respect to the function f(x, y) if Exf(Xt, y) = Eyf(x, Yt for all x ε{lunate} X, y ε{lunate} Y, t ≥ 0. It is shown that this duality reverses the role of entrance and exit laws for the processes, and that two previously published results of the authors are dual in precisely this sense. The duality relation for the function f(x, y) = 1{x is established for one-dimensional diffusions, and several new results on entrance and exit laws for diffusions, birth-death processes, and discrete time birth-death chains are obtained.
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U2 - 10.1016/0304-4149(84)90015-2
DO - 10.1016/0304-4149(84)90015-2
M3 - Article
AN - SCOPUS:0043086152
SN - 0304-4149
VL - 16
SP - 141
EP - 156
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 2
ER -