An introduction to WKB analysis III

In 1990's Aoki-Kawai-Takei investigated the traditional Painlev$'e$
equations $(P_{J})$ from a veiw point of the exact WKB analysis and
they succeeded in giving the concrete description of the Stokes phenomenon
and the connection formula for $(P_{J})$ $(J = I, II, ¥dots, VI)$.
Since this success, the research to analyze the higher order Painlev$'e$
equations has been progressed. In this talk, we first recall the theory
of the exact WKB analysis for Painlev$'e$ equations with a large parameter
and we discuss the instanton-type solutions which are expected to be
suitable formal solutions for the description of the connection problems.