Potential readers include those who wish to build up mathematical bases to deal with high-frequency data in mathematical finance and those who wish to learn the theoretical background for Cox's regression model in survival analysisIntuitive interpretations and concrete usages of fundamental theorems in martingale theoryRelatively new theorems in asymptotic statistics presented in a completely self-contained way.Highlight of the monograph is Chapters 8-10 dealing with Z-estimators and related topics