Although the English translation uses the verb "I live", the more literal translation would use "I am living" (which is also an accepted answer). If I were to be asked to translate "I live in my own house", I would have use the Turkish present simple: "Ben kendi evimde yaşarım".
I have noticed that there seems to be a few situations where the use of the present simple in English doesn't seem to default to the use of the present simple in Turkish, but rather the present continuous.
What's the difference in meaning here between saying:
Ben kendi evimde yaşıyorum
Ben kendi evimde yaşarım?
the aorist/habitual tense is usually used with frequential adverbs such as always, usually, often, rarely, sometimes and never. it implies a repetition and refers to a wider spectrum of time. and you won't actually use stative verbs in english (live, love, know, mean) in this tense because they don't imply a repetition. so, ben kendi evimde yaşarım is not a sentence that a normal Turk would use in this sense :) But it's used in literature. Let me sum its usage in modern language (except literature)
with some constructions such as if (-se/-sa) and while/as (-iken)
While I was watching T.V. I cleaned up my room. - Televizyon izlerken odamı topladım.
If he comes here, call me out. - Buraya gelirse beni çağırın.
In order to make statements more formal or state general facts you use the aorist tense (-er/-ar) or (-mektedir/-maktadır) This is often preferred by encyclopedias and other formal texts. With to be copula you do this by adding -dir.
Present tense in formal language
Metrobüsler sadece duraklarda durur/durmaktadır. - Metrobuses only stop at the stations.
compare: Metrobüs bugün ücretsizdir. - Metrobuses are today free.
Stating general facts
Güneş doğudan doğar/doğmaktadır. - The sun rises in the east.
compare: The sun is a star. - Güneş bir yıldızdır.
- Aorist tense is frequently used as a future tense. If you say YOU will do something (you emphasize your will to do that) you use aorist tense
Kapıya ben bakarım. - I will answer the door.
If you want to make a guess about the future you can again use the aorist tense.
Yarın gelir. -> She will (probably) come tomorrow.
Bence onu görmeyiz -> I think we won't see him.
Belki yemek yersin. -> Maybe you will eat.
- It is also used with frequential adverbs as I mentioned above. However, Şimdiki Zaman (-yor) is more preferred in daily speech.
O hiç sinemaya gitmez. - He never goes to the movies.
Bazen kitap okurum. - Sometimes I read book.
Burası genellikle kalabalıktır/kalabalık olur. - This place is usually crowded.
I have not gotten the impression that "kendi" implies ownership in the sense of having-the-deed-to-property; it is more like a primary-possessory-interest. I can see a difference between living in a place provided by someone else (your parents, the owner of the place who rents a room to you, etc.) -- which you still might call benim evim (my home) because you live there -- and living in a place that you are responsible for (whether you bought it or rented it, and whether it is a "house" or apartment) -- which could be benim kendi evim (my own home), even if you let other people live there with you.