Supplementary Problems
摘要
The list below contains problems which are related to all chapters of the book. Some of them are numerical and some others are pure theoretical, but in any case, they are help both students and instructors. Students can improve their understanding and scope. Instructors can transform most of the problems for teaching and examination purposes. The following references might be useful to create detailed solutions (see Baldi, Introduction through theory and exercises. 2017; Borodin, Stochastic processes, 2018; Çinlar, Probability and stochastics, 2011; Durrett, Essentials of stochastic processes, 2018; Eberlein and Kallsen, Mathematical finance, 2019; Etheridge, A course in financial calculus, 2002; Ikeda and Watanabe, Stochastic differential equations and diffusion processes, 1989; Jacod and Protter, Probability essentials, 2003; Kallianpur and Karandikar, Introduction to option pricing theory, 2012; Karatzas and Shreve, Brownian motion and stochastic calculus, 1998; Klebaner, Introduction to stochastic calculus with applications, 2012; Krylov, Introduction to the theory of random processes, 2002; Krylov, Controlled diffusion processes, 1980; Lamberton and Lapeyre, Introduction to stochastic calculus applied to finance, 1996; Le Gall, Brownian motion, martingales, and stochastic calculus, 2016; Melnikov, Theory Probab Appl 24(1):146–149, 1979; Melnikov, Sbornik Math 38(3):381–394, 1981; Melnikov, Russian Math Surv 51(5):43–136, 1996; Meyer, Probability and potential, 1966; Øksendal, Stochastic differential equations, 2000; Revuz and Yor, Continuous martingales and Brownian motion, 1999; Valkeila and Melnikov, Theory Probab Appl 44(2):333–360, 2000; Wentzell, A course in the theory of stochastic processes, 1981, and Williams, Probability and martingales, 1991).