In order to get a feeling for the reflected Bessel process the script [1] is a really nice resource.
Nevertheless, I feel a reluctance to use it as a reference, since
- it is not an official and "for all time" available publication, and may be altered in the future
- due to its conciseness it has a lack of details
- it is somehow inconvient for me to navigate through it
The points I am interested in are:
- generally a construction and definition of the reflected Bessel process, see p.29 of [1]
- the transition density, see p.29, eq. (36) of [1],
- for which parameters the process hits zero, see p.6, Proposition 2.1 of [1]
- that it is strong Markov, has continuous paths and solves a SDE up to the first hitting time of zero
References for the different bullet points can be found in various places, but I found them nowhere together, and especially for Bessel processes in one place except in [1]. For example:
- one can find corresponding statements regarding 1. and 3.,4. about the squared Bessel process in the blog [2]
- regarding 3.,4. it is also possible to view the process more generally as diffusion in an interval and apply Feller's Test for Explosions, see p.342 in [3]
- in fact, regarding 2., for me it is only relevant, that the process has a density w.r.t. Lebesgue measure. maybe more general situations as in this post Is the distribution of an Ito diffusion at time t absolutely continuous wrt Lebesgue measure? also work here
Question : Is there a book or monograph giving all these properties and more details?
[1] http://www.math.uchicago.edu/~lawler/bessel18new.pdf
[2] https://almostsuremath.com/2010/07/28/bessel-processes/
[3] Karatzas, Shreve - Brownian motion and stochastic calculus