Exercise 13.14 In the time-homogeneous case, the generator (13.43) is defined by where 2 (x)

Exercise 13.14 In the time-homogeneous case, the generator (13.43) is defined by

where σ²(x) ≥ ε > 0. Any solution to the equation Lf = 0 is called a harmonic function for L. Show that a positive harmonic function is given by

for some

c. Using this result, obtain a solution for Exercise 13.2.

Transcribed Image Text:

|L (x) = (x) fz(x) + 0 (x) fxx(x),