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Exit times of Brownian motion, harmonic majorization, and Hardy spaces. (English) Zbl 0372.60112


MSC:

60J65 Brownian motion
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
30D55 \(H^p\)-classes (MSC2000)
60G40 Stopping times; optimal stopping problems; gambling theory
31A35 Connections of harmonic functions with differential equations in two dimensions
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[1] Anderson, T. W., The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities, (Proc. Amer. Math. Soc., 6 (1955)), 170-176 · Zbl 0066.37402
[2] Baernstein, A., Integral means, univalent functions and circular symmetrization, Acta Math., 133, 139-169 (1974) · Zbl 0315.30021
[3] Baernstein, A.; Taylor, B. A., Spherical rearrangements, subharmonic functions, and ∗-functions in \(n\)-space, Duke Math. J., 43, 245-268 (1976) · Zbl 0331.31002
[4] C. Borell; C. Borell
[5] Burkholder, D. L., Distribution function inequalities for martingales, Ann. Probability, 1, 19-42 (1973) · Zbl 0301.60035
[6] Burkholder, D. L., \(H^p\) spaces and exit times of Brownian motion, Bull. Amer. Math. Soc., 81, 556-558 (1975) · Zbl 0321.60059
[7] Burkholder, D. L.; Gundy, R. F., Extrapolation and interpolation of quasi-linear operators on martingales, Acta Math., 124, 249-304 (1970) · Zbl 0223.60021
[8] Burkholder, D. L.; Gundy, R. F.; Silverstein, M. L., A maximal function characterization of the class \(H^p\), Trans. Amer. Math. Soc., 157, 137-153 (1971) · Zbl 0223.30048
[9] Doob, J. L., Stochastic Processes (1953), Wiley: Wiley New York · Zbl 0053.26802
[10] Doob, J. L., Seminartingales and subharmonic functions, Trans. Amer. Math. Soc., 77, 86-121 (1954) · Zbl 0059.12205
[11] Doob, J. L., Conformally invariant cluster value theory, Illinois J. Math., 5, 521-549 (1961) · Zbl 0196.42201
[12] Duren, P. L., Theory of \(H^p\) Spaces (1970), Academic Press: Academic Press New York · Zbl 0215.20203
[13] Dynkin, E. B.; Yushkevich, A. A., Markov Processes: Theorems and Problems (1969), Plenum: Plenum New York · Zbl 0073.34801
[14] Erdélyi, A.; Magnus, W.; Oberhettinger, F.; Tricomi, F. G., (Higher Transcendental Functions, Vol. I (1953), McGraw-Hill: McGraw-Hill New York) · Zbl 0052.29502
[15] Haliste, K., Estimates of harmonic measures, Ark. Mat., 6, 1-31 (1965) · Zbl 0178.13801
[16] Hansen, L. J., Hardy classes and ranges of functions, Michigan Math. J., 17, 235-248 (1970) · Zbl 0189.08602
[17] Hansen, L. J., Boundary values and mapping properties of \(H^p\) functions, Math. Z., 128, 189-194 (1972) · Zbl 0242.30033
[18] Helms, L. L., Introduction to Potential Theory (1969), Wiley-Interscíence: Wiley-Interscíence New York · Zbl 0188.17203
[19] Helson, H.; Sarason, D., Past and future, Math. Scand., 21, 5-16 (1967) · Zbl 0241.60029
[20] Hunt, G. A., Some theorems concerning Brownian motion, Trans. Amer. Math. Soc., 81, 294-319 (1956) · Zbl 0070.36601
[21] McKean, H. P., Stochastic Integrals (1969), Academic Press: Academic Press New York · Zbl 0191.46603
[22] Meyer, P. A., Probability and Potentials (1966), Blaisdell: Blaisdell Waltham, Mass. · Zbl 0138.10401
[23] Neuwirth, J.; Newman, D. J., Positive
((H^{12}\) functions are constants, (Proc. Amer. Math. Soc., 18 (1967)), 958 · Zbl 0183.34304
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