A semimartingale is a type of stochastic process that is important in the study of stochastic calculus and financial mathematics. It generalizes the concept of martingales and allows for the inclusion of processes that have finite variation as well as those that exhibit jumps, making it versatile for modeling various types of random phenomena. Semimartingales serve as the foundational building blocks for defining the Itô integral and solving stochastic differential equations, highlighting their significance in both theoretical and practical applications.
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