Article PDF
Avoid common mistakes on your manuscript.
References
Bellman, R., Harris, T.: Recurrence times for the Ehrenfest model. Pacific J. Math. 1, 179–193 (1951)
Bramson, M.: Maximal displacement of branching Brownian motion. Comm. Pure Appl. Math. 31, 531–581 (1978)
Breiman, L.: First exit times from a square root boundary. Proc. 5th Berkeley Sympos. Math. Statist. Probab. 2, pp. 9–16: Univ. Calif. 1966
Ito, K., McKean, H.P.: Diffusion processes and their sample paths. Berlin, Heidelberg, New York: Springer 1965
Kesten, H.: Branching Brownian motion with absorption. Stoch. Process. Appl. 7, 9–47 (1978)
Kolmogorov, A., Petrovsky, I., Piskunov, N.: Étude de l'équation de la diffusion avec croissance de la quantité de la matière et son application à un problème biologique. Moscow Univ. Bull. Math. 1, 1–25 (1937)
Lai, T., Wijsman, R.: First exit time of a random walk from the bounds f(n)±g(n), with applications. Ann. Probab. 7, 672–692 (1979)
McKean, H.: Elementary solutions for certain parabolic partial differential equations. Trans. Amer. Math. Soc. 82, 519–548 (1956)
McKean, H.: Application of Brownian motion to the equation of Kolmogorov-Petrovskii-Piskunov. Comm. Pure Appl. Math. 28, 323–331 (1975)
Portnoy, S.: Probability bounds for first exits through moving boundaries. Ann. Probab. 6, 106–117 (1978)
Stokes, A.: Nonlinear diffusion wave shapes generated by possibly finite initial disturbances. J. Math. Anal. Appl. 61, 370–381 (1977)
Titchmarsh, E.: Eigenfunction expansions I. Oxford: Oxford Univ. Press 1946.
Uchiyama, K.: The behavior of solutions of some non-linear diffusion equations for large time. J. Math. Kyoto Univ. 18, 453–508 (1978)
Whittaker, E., Watson, G.: Modern analysis. New York: Macmillan 1943
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Uchiyama, K. Brownian first exit from and sojourn over one sided moving boundary and application. Z. Wahrscheinlichkeitstheorie verw Gebiete 54, 75–116 (1980). https://doi.org/10.1007/BF00535355
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00535355