TY - JOUR
T1 - On a result of C. Mueller and E. Perkins
AU - Krylov, N. V.
PY - 1997/8
Y1 - 1997/8
N2 - 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.
AB - 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.
KW - Solutions with compact support
KW - Two-parameter white noise
UR - http://www.scopus.com/inward/record.url?scp=0031477168&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0031477168&partnerID=8YFLogxK
U2 - 10.1007/s004400050120
DO - 10.1007/s004400050120
M3 - Article
AN - SCOPUS:0031477168
SN - 0178-8051
VL - 108
SP - 543
EP - 557
JO - Probability Theory and Related Fields
JF - Probability Theory and Related Fields
IS - 4
ER -