I suggest you start with either of these books if you want to understand the fundamentals:

https://dl.acm.org/doi/book/10.5555/26887

https://www.springer.com/gp/book/9780387901558

Hope this helps

Stochastic models have low control, but must be highly parameterised with empirical data, which are randomly driven by appropriate statistical distributions

I recommend the book: Theory of Stochastic Processes, by Cox and Miller.

My recommendations are:

https://www.springer.com/gp/book/9783319774886

https://www.springer.com/gp/book/9783319248516

I suggest Stochastic Differential Equations - An Introduction with Applications, by Bernt Øksendal, https://www.springer.com/gp/book/9783540047582

You may find the following texts useful:

(1) Applied Stochastic Control of Jump Diffusions, by Bernt Øksendal and Agnes Sulem,

https://www.springer.com/gp/book/9783030027797

(2) Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations, by Italo Capuzzo Dolcetta and Martino Bardi, https://www.springer.com/gp/book/9780817647544

Dear Kristoffer,

maybe look at:

1) G. Peskir and A. N. Shiryaev. Optimal stopping and free-boundary prob-

lems. Springer, 2006.

2) H. V. Poor and O. Hadjiliadis. Quickest detection. Cambridge University

Press, 2008.

3) W. A. Shewhart. Economic control of quality of manufactured product.

Macmillan And Co Ltd, London, 1931.

Best regards

Zbigniew Michna

You can also look at "Continuous-time Stochastic Control and Optimization with Financial Applications by Huyen Pham @ Andrew Omame

Try to give a look to the videos uploaded on youtube by the Instituto de Matemática Pura e Aplicada.

There are nice lectures on Stochastic Optimal Control taught by Hasnaa Zidani, a professor at Paris-Saclay University.