Numerical solution of a parabolic free boundary problem arising in statistical decision theory

Author:
Gary G. Sackett

Journal:
Math. Comp. **25** (1971), 425-434

MSC:
Primary 65N35

DOI:
https://doi.org/10.1090/S0025-5718-1971-0300473-9

MathSciNet review:
0300473

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Abstract: A parabolic free boundary problem which arises in a statistical decision setting is reduced to a free boundary problem for the heat equation which is amenable to numerical solution by the method of lines. An algorithm is given and the apparently globally converging results are compared with the asymptotic expansions of H. Chernoff and J. Breakwell.

**[1]**John Breakwell and Herman Chernoff,*Sequential tests for the mean of a normal distribution. II. (Large 𝑡)*, Ann. Math. Statist.**35**(1964), 162–173. MR**0158456**, https://doi.org/10.1214/aoms/1177703738**[2]**Herman Chernoff,*Sequential tests for the mean of a normal distribution*, Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. I, Univ. California Press, Berkeley, Calif., 1961, pp. 79–91. MR**0131941****[3]**Herman Chernoff,*Sequential tests for the mean of a normal distribution. III. (Small 𝑡)*, Ann. Math. Statist**36**(1965), 28–54. MR**0170442**, https://doi.org/10.1214/aoms/1177700269**[4]**Nguyen Dinh Chi (Thi), ``On a free boundary problem for a parabolic equation,''*Vestnik Moskov. Univ. Ser. Math. Mech.*, No. 2, 1966, pp. 40-54. (Russian)**[5]**Erich Rothe,*Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler Randwertaufgaben*, Math. Ann.**102**(1930), no. 1, 650–670 (German). MR**1512599**, https://doi.org/10.1007/BF01782368**[6]**Gary G. Sackett,*An implicit free boundary problem for the heat equation*, SIAM J. Numer. Anal.**8**(1971), 80–96. MR**0283423**, https://doi.org/10.1137/0708011**[7]**B. Sherman,*Some Comments on Free Boundary Problems for Parabolic Equations Arising in Statistical Decision Theory*, Rocketdyne Research Report #66-24, 1966.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1971-0300473-9

Keywords:
Free boundary,
method of lines,
Bayes risk

Article copyright:
© Copyright 1971
American Mathematical Society