Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 2 , pp. 379--384

ON THE GAUGE FOR THE NEUMANN PROBLEM IN THE HALF SPACE

By

S. RAMASUBRAMANIAN, Indian Statistical Institute

SUMMARY. We consider the gauge function G for the Neumann problem for D +q in the half space D={(a , x) Î Rd : a > 0}, where q is independent of and is periodic in x. It is shown that if G , then G is a bounded continuous function on Cl(D). If $H(x)=\int_0^{\infty}G(\alpha, x)d\alpha \neq \infty$ , it is shown that the corresponding Feyman-Kac semi-group decays exponentially.

AMS(1991) subject classification. Primary 60J65; secondary 60J45,60H30.

Key words and phrases. Renewal process, Skorohod embedding Theorem, Wiener process.

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