## 論文リスト

1. Limit theorems for stochastic flows of diffeomorphisms of jump type (with I.Shigekawa), Z. Wahr., vol.69, No.4 (1985), 507--540.

2. Convergence of driven flows of diffeomorphisms, Stochastics, vol. 18, No.3+4 (1986), 343--355.

3. Limit theorems for stochastic processes of jump type as current valued processes, Bull. Fac. General Education, Gifu Univ., vol. 22 (1987), 101--105.

4. Coalescing stochastic flows on the real line, Osaka J. Math., vol. 26, No.1 (1989), 139--158.

5. The short time asymptotics of the traces of the heat kernels for the magnetic Schroedinger operators, J. Math. Soc. Japan, vol. 42, No.4 (1990), 677--689.

6. Classical and non-classical eigenvalue asymptotics for magnetic Schroedinger operators, J. Func. Anal., vol. 95, No.2 (1991), 460--482.

7. Short time asymptotics for the traces of heat kernels of Schroedinger operators with magnetic fields (with N.Ikeda), Bull. Sci. math., vol. 116, No.1 (1992), 53--66.

8. 磁場をもつ Schoroedinger 作用素に対する固有値の漸近分布, 数学 44 巻, 4 号 (1992), 320--329.

9. The asymptotic distributions of the eigenvalues for the Schroedinger operators with magnetic fields, in Asymptotic Problems in Probability Theory: Wiener Functionals and Asymptotics, Ed. by K.D. Elworthy and N. Ikeda, 169--193, Longman, New York, 1993.

10. On the integrated density of states for the Schroedinger operators with certain electromagnetic fields, J. Math. Soc. Japan, vol. 45, No.2 (1993), 197--214.

11. Semiclassical asymptotics of eigenvalue distributions for Schroedinger operators with magnetic fields, Comm. P.D.E., vol. 19, No.5 ¥& 6 (1994), 719--750.

12. Semiclassical asymptotics of eigenvalues for Schroedinger operators with magnetic fields, J. Func. Anal., vol. 129, No.1 (1995), 168--190.

13. Quadratic Hamiltonians and associated orthogonal polynomials, J. Func. Anal., vol. 136, No.1 (1996), 214--225.

14. Spectral analysis of Schroedinger operators with magnetic fields (with N.Ueki), J. Func. Anal., vol. 140, No.1 (1996), 218--255.

15. On Bougerol and Dufresne's identities for exponential Brownian functionals (with M.Yor), Proc. Japan Acad., vol. 74, Ser.A, No.10 (1998), 152--155.

16. Brownian motion on the hyperbolic plane and Selberg trace formula (with N.Ikeda), J. Func. Anal., vol. 163, No.1 (1999), 63--110.

17. A version of Pitman's 2M-X theorem for geometric Brownian motions (with M.Yor), C. R. Acad. Sc. Paris S¥'erie I, t. 328 (1999), 1067--1074.

18. Some changes of probabilities related to a geometric Brownian version of Pitman's 2M-X theorem (with M.Yor), Elect. Comm. Prob., vol. 4 (1999), 15--23.

19. An analogue of Pitman's 2M-X theorem for exponential Brownian functionals, Part I: A time inversion approach (with M.Yor), Nagoya Math. J., vol. 159 (2000), 125--166.

20. On positive and negative moments of the integrals of geometric Brownian motions (with C.Donati-Martin and M.Yor), Stat. Prob. Lett., vol. 49 (2000), 45--52.

21. Applications of the theory of the metaplectic representation to quadratic Hamiltonians on the two-dimensional Euclidean space (with N.Ueki), J. Math. Soc. Japan, vol. 52, No.2 (2000), 269--292.

22. On striking identities about the exponential functionals of the Brownian bridge and Brownian motion (with C.Donati-Martin and M.Yor), Periodica Math. Hung., vol. 41, No.1--2 (2000), 103--119.

23. A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration (with M.Yor), Osaka J. Math., vol. 38 (2001), 383--398.

24. An analogue of Pitman's 2M-X theorem for exponential Brownian functionals, Part II: the role of generalized inverse Gaussian distributions (with M.Yor), Nagoya Math. J., vol. 162 (2001), 65--86.

25. On a triplet of exponential Brownian functionals (with L.Alili and T.Shiraishi), Sem. Prob. XXXV, Lecture Notes in Math. vol. 1755, 396--415, Springer, Berlin, 2001.

26. The law of geometric Brownian motion, and its integral, revisted; application to conditional moments (with C.Donati-Martin and M.Yor), in Mathematical Finance, Bachelier Congress 2000, Selected Papers, 221--243, ed. by H.Geman, D.Madan, S.Pliska and T.Vorst, Springer, 2001.

27. Some absolute continuity relationships for certain anticipative transformations of geometric Brownian motions (with C.Donati-Martin and M.Yor), Publ. RIMS Kyoto Univ., vol. 37, No.3 (2001), 295--326.

28. Subordinators related to the exponential functionals of Brownian bridges and explicit formulae for the semigroup of hyperbolic Brownian motions (with L.Nguyen and M.Yor), in Stochastic Processes and Related Topics, 213--235, ed. by R.Buckdahn, H.Engelbert and M.Yor, Gordon and Breach, 2001.

29. Closed form formulae for the heat kernels and the Green functions for the Laplacians on the symmetric spaces of rank one, Bull. Sci. math., vol. 125, No.6--7 (2001), 553--581.

30. Wiener functionals of second order and their L¥'evy measures (with S.Taniguchi), Electr. J. Prob., Vol. 7 (2002), Paper no. 14, pages 1-30.

31. Interpretation via Brownian motion of some independence properties between GIG and gamma variables (with M.Yor), Stat. Prob. Lett., vol. 61 (2003), 253--259.

32. On Dufresne's relation between the probability laws of exponential functionals of Brownian motions with different drifts, J. Appl. Prob., vol. 35 (2003), 184--206.

33. Markov or non-Markov property of cM-X processes (with Y.Ogura), J. Math. Soc. Japan, vol. 56 (2004), 519--540.

34. Some properties of the Wishart processes and a matrix extension of the Hartman-Watson laws (with C.Donati-Martin, Y.Doumerc and M.Yor), Publ. RIMS, Kyoto Univ., vol. 40 (2004), 1385--1412.

35. Exponential functionals of Brownian motion, I: Probability laws at fixed time (with M.Yor), Probability Surveys, vol. 2 (2005), 312--347.

36. Exponential functionals of Brownian motion, II: Some related diffusion processes (with M.Yor), Probability Surveys, vol. 2 (2005), 348--384.

37. Horizontal lift of the Brownian motion on the hyperbolic plane and the Selberg trace formula, J. Func. Anal., vol. 244 (2007), 565--578.

38. Tree structured independence for exponential Brownian functionals (with J. Weso¥l owski and P. Witkowski), Stochastic Process. Appl., vol. 119 (2009), no. 10, 3798--3815.

39. Limiting behaviors of the Brownian motions on hyperbolic spaces, Colloq. Math., vol. 119 (2010), no. 2, 193--215.

40. The probability distribution of the first hitting time of Bessel processes (with Y. Hamana), to appear in Trans. AMS. (available at arXiv:1106.6132)

41. The probability densities of the first hitting times of Bessel processes (with Y. Hamana), J. Math-for-Industry, Vol. 4 (2012B-2), pp. 91--95.

42. Asymptotics of the probability distributions of the first hitting times of Bessel processes (with Y. Hamana), Electron. Commun. Probab., Vol. 19 (2014), no. 5, pp. 1--5.

43. The Kolmogorov operator and classical mechanics (with N. Ikeda), Sem. de Probabilites XLVII, ed. by C.Donati-Martin, A.Lejay, A.Rouault, Lecture Notes in Math., 2137, 497--504, Springer-Verlag, 2015.

44. Hitting times of Bessel processes, volume of the Wiener sausages and zeros of Macdonald functions (with Y. Hamana), J. Math. Soc. Japan, Vol. 68 no. 4 (2016), (available at arXiv:1302.4526v1)

45. Hitting times to spheres of Brownian motions with and without drifts (with Y. Hamana), Proc. Amer. Math. Soc., {\bf 144} no. 12 (2016), 5385--5396. (available at arXiv:1504.03043)

46. A formula for the expected volume of the Wiener sausage with constant drift (with Y. Hamana), to appear in Forum Math., (available at arXiv:1512.03514)

47. On the zeros of the Macdonald functions (with T. Shirai and Y. Hamana), preprint. (available at arXiv:1302.5154)

48. Precise asymptotic formulae for the first hitting times of Bessel processes (with Hamana), submitted.

### その他

1. 数理統計入門 （宮原孝夫氏と共著），学術図書，1990.

2. Asymptotic Distributions of Eigenvalues for Schroedinger Operators with Magnetic Fields, Suugaku Expositions, vol. 161 (1994), 123--134. (論文 8 の英訳)

3. 経路空間上の積分と跡公式，数理科学 1999 年 3 月号, 23--30 (別冊・数理科学「双対性の世界」，2007 年 4 月，に再録)

4. 確率論とラプラシアン(小倉幸雄氏と共著)，数学の楽しみ，No. 12, 39--55.

5. 応用のための確率論・確率過程，Introduction to Probability Theory and Stochastic Processes, SGC ライブラリ--３６，サイエンス社，2004.

6. ブラウン運動(池田信行氏，谷口説男氏と共著)，確率論ハンドブック(伊藤清企画・監修，渡辺信三/重川一郎編)，57--111，2012.

7. 確率解析(谷口説男氏と共著)，培風館, 2013．

8. 確率・統計の基礎，学術図書，2014.

9. 解析学入門(市原直幸氏，増田哲氏と共著)，培風館，2016.

10. Stochastic Analysis (with S.taniguchi), Cambridge Univ. Press, 2017.