Stochastic Integration with Jumps

Focusing on stochastic processes with jumps and random measures, this book explores their applications in financial mathematics and signal processing. It presents a unified approach to stochastic integration theory for semimartingales and random measures, introducing innovative predictable controlling devices. The text covers stochastic differential equations, their stability, and numerical approximations, while highlighting key concepts such as Dominated Convergence Theorem and Egoroff's Theorem. It also provides analogs to ordinary integration theory, including previsible envelopes and algorithms for computing stochastic integrals.