Explicit representation of the Skorokhod map with time dependent boundaries

• Autorzy: Slaby M.
• Języki publikacji: EN

Abstrakty

EN

An explicit formula for the Skorokhod type reflection map for real-valued càdlàg functions is developed in the general case of constraining set [α,β], where α and ,β are not constant but change with time. In addition, a number of properties of the reflection map, including continuity and Lipschitz conditions under uniform, J₁ and M₁ metrics, are studied.

Słowa kluczowe

EN

Skorokhod map; Skorokhod problem; reflection map; double reflection map

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2010
• Tom: Vol. 30, Fasc. 1
• Strony: 29--60
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Slaby M.

• Department of Mathematics, CS and Physics, Fairleigh Dickinson University, 285 Madison Ave. M-AB2-02, Madison, NJ, 07940, USA

Bibliografia

• [1] S. V. Anulova and R. Sh. Liptser, Diffusion approximations for processes with normal reflection, Theory Probab. Appl. 35 (1990), pp. 411-423.
• [2] K. Burdzy, W. Kang and K. Ramanan, The Skorokhod problem in a time-dependent interval, Stochastic Process. Appl. 119 (2009), pp. 428-452.
• [3] P. Depuis and H. Ishii, On Lipschitz continuity of the solution mapping to the Skorokhod problem; with application, Stochastics 35 (1991), pp. 31-62.
• [4] L. Kruk, J. Lehoczky, K. Ramanan and S. Shreve, An explicit formula for the Skorokhod map on [0; a], Ann. Probab. 35 (2007), pp. 1740-1768.
• [5] K. Ramanan, Reflected diffusions defined via the extended Skorokhod map, Electron. J. Probab. 11 (2006), pp. 934-992.
• [6] K. Ramanan and M. Reiman, The heavy traffic limit of an unbalanced generalized processor sharing model, Ann. Appl. Probab. 18 (2008), pp. 22-58.
• [7] A. V. Skorokhod, Stochastic equations for diffusions in a bounded region, Theory Probab. Appl. 6 (1961), pp. 264-274.
• [8] H. Tanaka, Stochastic differential equations with reflecting boundary condition in convex regions, Hiroshima Math. J. 9 (1979), pp. 163-177.
• [9] W. Whitt, An Introduction to Stochastic-process Limits and Their Application to Queues, Springer, New York 2002.