On Stochastic Differential Equations

Focusing on stochastic differential equations, the work explores the construction of Markov processes through transition probability laws. Kiyosi Ito discusses the conditions under which solutions exist and are unique, referencing W. Feller's work on continuous and discontinuous cases. The text delves into the measurability and regularity of these processes, citing contributions from J. L. Doob and others. It aims to construct solutions to stochastic differential equations while rigorously addressing the properties of these solutions within the framework of stochastic calculus.