Hiroshima Mathematical Journal

Stochastic differential equations with reflecting boundary condition in convex regions

Hiroshi Tanaka
Source: Hiroshima Math. J. Volume 9, Number 1 (1979), 163-177.
First Page: Show Hide
Primary Subjects: 60H10
Secondary Subjects: 60J60
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.hmj/1206135203
Mathematical Reviews number (MathSciNet): MR529332
Zentralblatt MATH identifier: 0423.60055

References

[1] N. Ikeda, On the construction of two-dimensional diffusion processes satisfying Wentzels boundary conditions and its application to boundary value problems, Mem. Coll. Sci. Univ. Kyoto, 33 (1961), 367-427.
Zentralblatt MATH: 0102.13903
Mathematical Reviews (MathSciNet): MR126883
[2] H. P. McKean, A. Skorohod's integral equation for a reflecting barrier diffusion, J. Math. Kyoto Univ., 3 (1963), 86-88.
Zentralblatt MATH: 0202.46601
Mathematical Reviews (MathSciNet): MR157406
[3] H. P. McKean, Stochastic Integrals, Academic Press, 1969.
Zentralblatt MATH: 0191.46603
Mathematical Reviews (MathSciNet): MR247684
[4] A. V. Skorohod, Stochastic equations for diffusion processes in a bounded region 1, 2, Theor. Veroyatnost. i Primenen. 6 (1961), 264-274; 7 (1962), 3-23.
Zentralblatt MATH: 0215.53501
[5] A. V. Skorohod, Studies in the Theory of Random Processes, Addison Wesley, 1965.
Zentralblatt MATH: 0146.37701
Mathematical Reviews (MathSciNet): MR185620
[6] D. W. Stroock and S. R. S. Varadhan, Diffusion processes with boundary conditions, Comm. Pure Appl. Math., 24 (1971), 147-225.
Zentralblatt MATH: 0227.76131
Mathematical Reviews (MathSciNet): MR277037
[7] M. Tsuchiya, On the stochastic differential equation for a two-dimensional Brownian motion with boundary condition, to appear.
Zentralblatt MATH: 0444.60066
Mathematical Reviews (MathSciNet): MR567417
[8] S. Watanabe, On stochastic differential equations for multi-dimensional diffusion processes with boundary conditions, J. Math Kyoto Univ., 11 (1971), 169-180.
Zentralblatt MATH: 0212.20203
Mathematical Reviews (MathSciNet): MR275537
[9] S. Watanabe and T. Yamada, On the uniqueness of solutions of stochastic differential equations II, J. Math. Kyoto Univ., 11 (1971), 553-563.
Zentralblatt MATH: 0229.60039
Mathematical Reviews (MathSciNet): MR288876

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Hiroshima Mathematical Journal

Hiroshima Mathematical Journal