Quantitative analysis of reversible Markov processes and the theory of stochastic stopping game

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The head investigator collaborated with J. Ying and X. Fang to characterize all regular Dirichlet subspaces of a one-dimensional Sobolev space in terms of a family of scale functions in the joint paper from Osaka J. Math. He also successfully collaborated with J. Ying and P. He and then with J. Ying and Z.Q.Chen to characterize the jumping measure of the time changed processes of a symmetric diffusion and a most general symmetric Markov process in terms of the Feller measure determined by the minimal process, and the results are being published in two papers from Annales of Probability in USA. He further collaborates with H. Tanaka to extend an old result of K. Ito by construction a symmetric diffusion by piecing together excursions away from a point in a joint paper being published in a famous French journal.