I am currently doing a course in Stochastic Processes that uses the book "Adventures in Stochastic Processes" by Sidney I. Resnick. The topics covered in the book are as follows:
Discrete Index Sets/ Discrete State Spaces, Markov Chains, Renewal Theory, Point Processes, Continuous Time Markov Chains, Brownian Motion and General Random Walk.
The author describes this book as a "first year graduate text for courses usually called Stochastic Processes (perhaps amended by the words "Apploed" or "Introduction to . . . ") or Applied Probability or sometimes Stochastic Modeling."
I am currently a junior math major and I just completed Probability theory. The topics covered in this class interest me and I am thinking of taking a few more classes related to stochastic processes in the next two years. I will be taking Real Analysis I (Royden: This course also covers Lebegue Integrals) next semester and would love to take at least one more course related to Stochastic Processes after the completion of Analysis. Can you please let me know where I will stand after the completion of this Stochastic Processes course that I am currently taking? What would be the next logical class for me to take? Also, what is the difference between a Stochastic Processes class and Stochastic Calculus? I see both of these classes on the internet and I was wondering if the two terms were interchangeable. Do they provide comparable levels of preparation for a class in Stochastic Differential Eq?
Thanks for your help in advance.