Summary.
The equation du=(au”+bu′+cu) dt+νu γ W(dx,dt) is considered for γ∈(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.
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Received: 6 September 1996 / In revised form: 12 February 1997
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Krylov, N. On a result of C. Mueller and E. Perkins. Probab Theory Relat Fields 108, 543–557 (1997). https://doi.org/10.1007/s004400050120
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DOI: https://doi.org/10.1007/s004400050120
- Key words and phrases: Two-parameter white noise
- solutions with compact support.
- Mathematics Subject Classification (1991): 60H15
- 35R60