All of these behaviors, i.e, jumping, digging, chasing and stealing are within the range of normal dog behaviors but dogs that are kept relatively inactive, may behave excessively in one or more of these ways, specially high energy dogs.
Separation anxiety is evident if a dog is jumping excessively as part of greeting. Digging can be associated with neurological disorders or abdominal pain.
Behavior and its symtoms are as follows
Jumping on people
During arrivals, departures or greetings
Exploring the contents of countertops
Along a fence line
In areas of recent gardening
At rodent holes
On interior flooring
Worn claws (nails)
Items displaced, hidden
Food items missing from surfaces (i.e., tables)