Oxidation
In the presence of oxygen, oxidation of the cellulose, in the insulation paper, breaks the polymer chains and produces by-products including water and acids. Acids promote hydrolysis as catalysts for the process. Water produced in these reactions promotes hydrolysis.
Oxygen, however, is not produced by the processes of hydrolysis, oxidation or pyrolysis, so any oxygen content in the oil enters from the atmosphere either during manufacture or through the breather system.
References
[1] Lelekakis, Nick, et al. “Ageing Rate of Paper Insulation Used in Power Transformers Part 2: Oil/Paper System with Medium and High Oxygen Concentration.” Ieee Transactions On Dielectrics And Electrical Insulation, vol. 19, no. 6, 2012, pp. 2009–2018.