Yes, you can depreciate the inherited property's basis (value) over the useful life of the property. This value is estimated by the fair market value at the time of the decedent's death, minus any estimated land value. Check to see if the executor of the estate used an alternate valuation date. Then you would use the FMV on the alternate valuation date. This would only make a difference if the value of the property changed considerably over the 6 months after the date of death.
The alternate valuation date falls six months after the date of death, and in some situations, using the alternate date dramatically reduces estate taxes. If the people handling the estate make that election, then your cost basis going forward will be the value of the property on that alternate date, rather than the date of death.
