The equation du = (au″+ bu′ + cu) dt + vuγ W(dx, dt) is considered for γ ε (0, 1). It is proved that u(t, ·) has compact support for all t ≥ 0 if u(0, ·) does. This result extends a result of C. Mueller and E. Perkins who considered the case a = 1, b = c = 0. The proof does not use the nonstandard analysis unlike the one by C. Mueller and E. Perkins.
- Solutions with compact support
- Two-parameter white noise