Bálint Tóth:
Conjugate Diffusions on R_+ and Generalized
Ray-Knight processes
We define the notion of conjugacy of a pair of
diffusions on the positive half-line R_+. Typical
examples of conjugate diffusions are pairs of squared Bessel
processes of generalized dimension δ, respectively
2-δ (the latter one being stopped at first hitting of
0). Using pairs of conjugate diffusions we construct
processes with a structure similar to the processes arising
in the Ray-Knight description of Brownian local time. These
generalized Ray-Knight processes arise naturally as
scaling limits of the local time of non-Markovian Random
walks. The main technical result of the paper sheds light
on the intimate probabilistic content of conjugacy.
balint@math-inst.hu