Not quite sure about the two youngest children in the emigration list. In the 1880 Census he is using the name John Peterson and only two chidren born in Norway listed are the two oldest,, Petter and Agnethe.
John Peterson in the 1880 United States Federal Census Name: John Peterson Age: 44 Birth Date: Abt 1836 Birthplace: Norway Home in 1880: Roscoe, Goodhue, Minnesota , USA Dwelling Number: 6 Race: White Gender: Male Relation to Head of House: Self (Head) Marital status: Married Spouse's name: Nellie Peterson Father's Birthplace: Norway Mother's Birthplace: Norway Occupation: Farm Laborer Neighbors: View others on page Household Members: Name Age John Peterson 44 Nellie Peterson 36 Peter Peterson 17 Agnes Peterson 13 Andrew Peterson 4 Olaf Peterson 2 Josephine Peterson 3/12
The wife of Johan Pedersen Finstuen was Penille Hansdatter. She was born July 24, 1843. Parents are Hans Xstiansen and Agnethe Andersdatter Gjerdahlen. A little hard to read the last name of Agnethe could be Arnesdatter"