Which sentence is written correctly?

Their dog has caused so many problems in your neighborhood.

They're dog has caused so many problems in your neighborhood.

There dog has caused so many problems in your neighborhood.

They're dog has caused so many problems in you're neighborhood

The sentence that is written correctly is, Their dog has caused so many problems in your neighborhood. The difference between the sentences is the correct use of the words their, they're and there. In this case, since it shows ownership (to the word dog), the correct word should be used is "their", a possessive pronoun.