A formula for the expected volume of the Wiener sausage with constant drift

References

[1] van den Berg M., Bolthausen E. and den Hollander F., Moderate deviations for the volume of the Wiener sausage, Ann. of Math. (2) 153 (2001), 355–406. 10.2307/2661345Search in Google Scholar

[2] Donsker M. D. and Varadhan S. R. S., Asymptotics for the Wiener sausage, Comm. Pure Appl. Math. 28 (1975), 525–565. 10.1002/cpa.3160280406Search in Google Scholar

[3] Getoor R. K., Some asymptotic formulas involving capacity, Z. Wahrscheinlichkeitstheor. Verw. Gebiete 4 (1965), 248–252. 10.1007/BF00533755Search in Google Scholar

[4] Hamana Y., Limit theorems for the Wiener sausage, Sugaku Expos. 18 (2005), 53–73. Search in Google Scholar

[5] Hamana Y., On the expected volume of the Wiener sausage, J. Math. Soc. Japan 62 (2010), 1113–1136. 10.2969/jmsj/06241113Search in Google Scholar

[6] Hamana Y., The expected volume and surface area of the Wiener sausage in odd dimensions, Osaka J. Math. 49 (2012), 853–868. Search in Google Scholar

[7] Hamana Y., Asymptotic expansion of the expected volume of the Wiener sausage in even dimensions, Kyushu J. Math. 70 (2016), 167–196. 10.2206/kyushujm.70.167Search in Google Scholar

[8] Hamana Y. and Kesten H., A large deviation result for the range of random walks and for the Wiener sausage, Probab. Theory Related Fields 120 (2001), 183–208. 10.1007/PL00008780Search in Google Scholar

[9] Hamana Y. and Matsumoto H., The probability distributions of the first hitting times of Bessel processes, Trans. Amer. Math. Soc. 365 (2013), 5237–5257. 10.1090/S0002-9947-2013-05799-6Search in Google Scholar

[10] Hamana Y. and Matsumoto H., Hitting times of Bessel processes, volume of Wiener sausages and zeros of Macdonald functions, J. Math. Soc. Japan, to appear. 10.2969/jmsj/06841615Search in Google Scholar

[11] Hamana Y. and Matsumoto H., Hitting times to spheres of Brownian motions with and without drifts, Proc. Amer. Math. Soc., to appear. 10.1090/proc/13136Search in Google Scholar

[12] Kac M. and Luttinger J. M., Bose–Einstein condensation in the presence of impurities II, J. Math. Phys. 15 (1974), 183–186. 10.1063/1.1666617Search in Google Scholar

[13] Itô K. and McKean, Jr. H. P., Diffusion Processes and Their Sample Paths, Springer, Berlin, 1974. Search in Google Scholar

[14] Lebedev N. N., Special Functions and Their Applications, Dover, New York, 1972. Search in Google Scholar

[15] Le Gall J. -F., Sur le temps local d’intersection du mouvement Brownien plan et la méthode de renormalisation de Varadhan, Séminaire de Probabilitiés XIX, Lecture Notes in Math. 1123, Springer, Berlin (1985), 314–331. 10.1007/BFb0075863Search in Google Scholar

[16] Le Gall J.-F., Fluctuation results for the Wiener sausage, Ann. Probab. 16 (1988), 991–1018. 10.1214/aop/1176991673Search in Google Scholar

[17] Le Gall J.-F., Sur une conjecture de M. Kac, Probab. Theory Related Fields 78 (1988), 389–402. 10.1007/BF00334202Search in Google Scholar

[18] Le Gall J.-F., Wiener sausage and self-intersection local times, J. Funct. Anal. 88 (1990), 299–341. 10.1016/0022-1236(90)90108-WSearch in Google Scholar

[19] Magnus W., Oberhettinger F. and Soni R. P., Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd ed., Springer, Berlin, 1966. 10.1007/978-3-662-11761-3Search in Google Scholar

[20] Port S. C., Asymptotic expansions for the expected volume of a stable sausage, Ann. Probab. 18 (1990), 492–523. 10.1214/aop/1176990842Search in Google Scholar

[21] Spitzer F., Electrostatic capacity, heat flow and Brownian motion, Z. Wahrscheinlichkeitstheor. Verw. Gebiete 3 (1964), 110–121. 10.1007/978-1-4612-0459-6_4Search in Google Scholar

[22] Spitzer F., Discussion of “Subadditive ergodic theory” by J. F. C. Kingman, Ann. Probab. 1 (1973), 904–905. 10.1214/aop/1176996798Search in Google Scholar

[23] Watson G. N., A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1995. Search in Google Scholar