robability with Applications in Engineering, Science, and Technology by Peter Olofsson and Thomas H. Ryff-Elementary Stochastic Calculus with Finance in View by Thomas Mikosch-Probability, Random Processes, and Statistical Analysis by Robert M. Gray-Probability and Measure Theory by Robert B. Ash-Theory of Point Processes by Daley and Vere-Jones-Stochastic Processes and Applications by David NualartFor advanced Ito calculus, some recommended books are:-Stochastic Differential Equations: An Introduction with Applications by Bernt Oksendal-An Introduction to Stochastic Differential Equations by Peter E. Kloeden and Eckhard Platen-Stochastic Calculus for Finance I: The Binomial Asset Pricing Model by Steven Shreve-Advanced Financial Modelling by Damiano Brigo and Fabio Mercurio-Stochastic Calculus for Finance II: Continuous-Time Models by Steven ShreveProbability theory is a branch of mathematics that deals with the study of random phenomena. It provides a framework for understanding and quantifying uncertainty and allows us to make predictions about the likelihood of different outcomes.
Ito calculus is a branch of mathematics that is used to study stochastic processes, which are systems that evolve over time in a random manner. It is a powerful tool for analyzing and understanding the behavior of these systems, and it has applications in fields such as finance, physics, and biology.
Probability theory has many practical applications, including risk assessment in finance, prediction of weather patterns, and analysis of medical data. It is also used in fields such as gambling, insurance, and genetics.
Yes, a strong foundation in mathematics is necessary to fully understand and appreciate advanced textbooks in probability and/or Ito calculus. These subjects require a solid understanding of calculus, linear algebra, and probability theory.
To improve your understanding of these subjects, it is important to have a strong mathematical background and to practice solving problems and working through examples. You can also attend lectures, join study groups, and seek guidance from experienced mathematicians or professors.