Hi. What is that you don't understand about "мой"? I don't really get the question. The verb "думать о" needs the following noun to be in the accusative case, and all the rest words that are realted to that noun have to be of the same case, so the pronoun is in the prepositional case.

Transitive and Intransitive verbs
А. Verbs that take a direct object are called transitive verbs. They are indicated by a "v.t." in the dictionary.
The direct object answers the question что? (what?) or кого? (whom?) asked after the verb and receives the action of the verb directly, without prepositions separating the verb from the receiver.
Study the following example:
1. Он читает газету. 1. He is reading a newspaper.
The verb (читает - is reading) is followed by the noun (газету - a newspaper) answering the question что? (what):
  • Он читает что? Answer: газету. - He is reading what? Answer: a newspaper.

The noun газету is in the Accusative case. The Accusative case expresses the direct object.
More examples of the transitive verbs followed by the direct object:
2. Она пишет статью. 1. She is writing an article.
3. Мы смотрим телевизор. 2. We are watching TV.
4. Я изучаю русский язык. 3. I'm studying Russian.
5. Они редко слушают музыку. 3. They listen to the music rarely.
Б. Verbs that do not take a direct object are called intransitive verbs. They are indicated by a "v.i." in the dictionary. An intransitive verb cannot take a direct object by definition.
Study the following example:
1. Он живёт в Москве. 1. He lives in Moscow.
The verb (живёт - lives) cannot be followed by a noun answering the question что? (what?). The question we ask is где? (where):
  • Он живёт где? Answer: в Москве. - He lives where? Answer: in Moscow.

The noun в Москве is in the Prepositional case, and it is the indirect object.
More examples of the intransitive verbs followed by the indirect object:
2. Она работает в университете. 2. She works at university.
3. Я всегда отдыхаю в воскресенье. 3. I always relax on Sunday.
Notes
  • Some verbs may be used both transitively and intransitively.
  • Some verbs are transitive in English but intransitive in Russian. Such verbs are to be mentioned and discussed later on.
a) "должно быть"; "Наверное"
Он, должно быть, голоден - He must be hungry.
Он, наверное, голоден - He is probably hungry.
b) "Причина" - cause; "Повод" - occasion.
Иван поссорился с подругой. Причиной ссоры было то, что он ее разлюбил, а поводом стал сломанный компьютер.
c) "Надо"; "Нужно"; "Должен/Должн-а/о/ы"
Надо = нужно = need to
Должен/Должн-а/о/ы = have to or must
d) "За"; "Для"
Depends on the context, way too many meanings.
e) "Нельзя" - imposible/not allowed, ; "Возможно" = possible/allowable
f) "Давно" - long ago; "Долго" - for long; "Долгое время" - for a long time
g) "Потом"; "Затем"; "Тогда"; "То"
Depends. Many meanings but they all but the last may mean "after". And all of them may mean "then".
h) "Как раз" - right; "Точно" - exectly
i) "Всё-таки" - after all; "Всё равно" - no matter what/regardless
Всё-таки ты пришел! - You are here after all!
Ты всё равно пришел! - You are here, no matter what.