リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「PATHWISE UNIQUENESS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY CAUCHY PROCESSES WITH DRIFT」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。
リケラボ

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

PATHWISE UNIQUENESS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY CAUCHY PROCESSES WITH DRIFT

Tsukada, Hiroshi 大阪大学 DOI:10.18910/83206

2021.07

概要

We consider one-dimensional stochastic differential equations driven by Cauchy processes with drift. This driving process is also known as a strictly 1-stable process. In this paper, we study the pathwise uniqueness of the solution to the stochastic differential equations under a non-Lipschitz condition on the diffusion coefficient.

論文の公開元へ

関連論文

関連論文をもっと見る

参考文献

[1] D. Applebaum: Levy Processes and Stochastic Calculus, 2nd ed., Cambridge University Press, Cambridge, ´ 2009.

[2] R.F. Bass: Stochastic differential equations driven by symmetric stable processes; in Seminaire de Proba- ´ bilites XXXVI, Lecture Notes in Math. ´ 1801, Springer, Berlin, 2003, 302–313.

[3] R.F. Bass, K. Burdzy and Z.Q. Chen: Stochastic differential equations driven by stable processes for which pathwise uniqueness fails, Stochastic Process. Appl. 111 (2004), 1–15.

[4] H.J. Engelbert and V.P. Kurenok: The Tanaka formula for symmetric stable processes with index α, 0 < α < 2, Theory Probab. Appl. 64 (2019), 264–289.

[5] N. Fournier: On pathwise uniqueness for stochastic differential equations driven by stable L´evy processes, Ann. Inst. Henri Poincare Probab. Stat. ´ 49 (2013), 138–159.

[6] N. Ikeda and S. Watanabe: Stochastic Differential Equations and Diffusion Processes, 2nd ed., NorthHolland Publishing Co., Amsterdam; Kodansha Ltd., Tokyo, 1989.

[7] J. Kallsen and A.N. Shiryaev: Time change representation of stochastic integrals, Theory Probab. Appl. 46 (2002), 522–528.

[8] T. Komatsu: On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations of jump type, Proc. Japan Acad. Ser. A Math. Sci. 58 (1982), 353–356.

[9] Z. Li and L. Mytnik: Strong solutions for stochastic differential equations with jumps, Ann. Inst. Henri Poincare Probab. Stat. ´ 47 (2011), 1055–1067.

[10] R. Situ: Theory of Stochastic Differential Equations with Jumps and Applications: Mathematical and Analytical Techniques with Applications to Engineering, Springer, New York, 2005.

[11] A. Takeuchi and H. Tsukada: Remark on pathwise uniqueness of stochastic differential equations driven by L´evy processes, Stoch. Anal. Appl. 37 (2019), 155–170.

[12] T. Yamada and S. Watanabe: On the uniqueness of solutions of stochastic differential equations, J. Math. Kyoto Univ. 11 (1971), 155–167.

[13] P.A. Zanzotto: On stochastic differential equations driven by a Cauchy process and other stable L´evy motions, Ann. Probab. 30 (2002), 802–825.

参考文献をもっと見る