gistfile1.json

$ aws lambda get-event-source --uuid my-events-uuid
{
    "Status": "OK",
    "UUID": "my-events-uuid",
    "LastModified": "2014-11-22T02:37:00.000+0000",
    "BatchSize": 1,
    "Parameters": {
        "InitialPositionInStream": "TRIM_HORIZON"
    },
    "Role": "arn:aws:iam::acct-number:role/lambda_exec_role",
    "EventSource": "arn:aws:kinesis:us-west-2:acct-number:stream/lambda-source",
    "IsActive": "true",
    "FunctionName": "Kinesis"
}

lambda_exec_role's policy

{
  "Version": "2012-10-17",
  "Statement": [
    {
      "Effect": "Allow",
      "Action": [
        "logs:*"
      ],
      "Resource": "arn:aws:logs:*:*:*"
    },
    {
      "Effect": "Allow",
      "Action": [
        "kinesis:*"
      ],
      "Resource": [
        "arn:aws:kinesis:*:*:stream/*"
      ]
    },
    {
      "Effect": "Allow",
      "Action": [
        "s3:GetObject",
        "s3:PutObject"
      ],
      "Resource": [
        "arn:aws:s3:::*"
      ]
    }
  ]
}