Density of Space-Time Distribution of Brownian First Hitting of a Disc and a Ball

Springer Science and Business Media LLC - Tập 44 Số 3 - Trang 497-541 - 2016
Kôhei Uchiyama1
1Department of Mathematics, Tokyo Institute of Technology, Oh-okayama, Meguro, Tokyo, 152-8551, Japan

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Tài liệu tham khảo

Byczkowski, T., Malecki, J., Ryznar, M.: Hitting times of Bessel processes. Potential Anal. 38, 753–786 (2013)

Carslaw, H.S., Jaeger, J.C.: Conduction of heat in solids. Clarrendon, Oxford (1992)

Erdélyi, A.: Tables of Integral Transforms, vol. I. McGraw-Hill, Inc (1954)

Hamana, Y., Matumoto, H.: The probability densities of the first hitting times of Bessel processes. J. Math-for-Ind 4B, 91–95 (2012)

Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes. North-Holland (1981)

Itô, K., McKean, H.P. Jr.: Diffusion processes and their sample paths. Springer (1965)

Karatzas, I., Shreve, S. E.: Brownian motion and stochastic calculus, 2nd ed. Springer (1991)

Revus, D., Yor, M.: Continuous martingales and Brownian motion, 3ed ed. Springer (1999)

Sommerfeld, A.: Partial differential equations in physics. Academic (1949)

Stein, E., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton Univ. Press (1971)

Titchmarsh, E.C.: Eigenfunction expansions, Part one, 2nd ed. Oxford University Press (1962)

Ten, J., Yor, M.: Local times and excursion theory for Brownian motion, LNM 2088. Springer (2013)

Uchiyama, K.: Asymptotic estimates of the distribution of Brownian hitting time of a disc. J. Theor. Probab. 25, 450–463 (2012). Erratum, J. Theor. Probab. 25 (2012), issue 3, 910–911

Uchiyama, K.: The expected area of Wiener sausage swept by a disk. Stoch. Proc. Appl. 123, 191–211 (2013)

Uchiyama, K.: Asymptotics of the densities of the first passage time distributions of Bessel diffusion. Trans. Amer. Math. Soc. 367, 2719–2742 (2015)

Uchiyama, K.: Brownian hitting distributions in space-time of bounded sets and the expected volume of Wiener sausage for Brownian bridges, available at arXiv: 1406.1307v3

Uchiyama, K.: Zeros of modified Bessel function of imaginary order and winding of planer Brownian motion, preprint

Uchiyama, K.: The expected volume of Wiener sausage for a Brownian bridge joining the origin to a point outside a parabolic region, RIMS Kokyuroku 1855. Probability Symposium 10–18 (2013)

Watson, G.N.: A treaties on the theory of Bessel functions, 2nd ed., Reprinted by Springer (1995)

Watson, N.A.: Introduction to heat potential theory, Mathematical surveys and monographs. AMS 182 (2012)