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2012 | 10 | 2 | 693-702

Tytuł artykułu

Numerical schemes for multivalued backward stochastic differential systems

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Języki publikacji

EN

Abstrakty

EN
We define approximation schemes for generalized backward stochastic differential systems, considered in the Markovian framework. More precisely, we propose a mixed approximation scheme for the following backward stochastic variational inequality: $$dY_t + F(t,X_t ,Y_t ,Z_t )dt \in \partial \phi (Y_t )dt + Z_t dW_t ,$$ where ∂φ is the subdifferential operator of a convex lower semicontinuous function φ and (X t)t∈[0;T] is the unique solution of a forward stochastic differential equation. We use an Euler type scheme for the system of decoupled forward-backward variational inequality in conjunction with Yosida approximation techniques.

Wydawca

Czasopismo

Rocznik

Tom

10

Numer

2

Strony

693-702

Opis fizyczny

Daty

wydano
2012-04-01
online
2012-01-18

Twórcy

  • Alexandru Ioan Cuza University
  • Alexandru Ioan Cuza University

Bibliografia

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  • [2] Bouchard B., Menozzi S., Strong approximations of BSDEs in a domain, Bernoulli, 2009, 15(4), 1117–1147 http://dx.doi.org/10.3150/08-BEJ181
  • [3] Bouchard B., Touzi N., Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations, Stochastic Process. Appl., 2004, 111(2), 175–206 http://dx.doi.org/10.1016/j.spa.2004.01.001
  • [4] Chitashvili R.J., Lazrieva N.L., Strong solutions of stochastic differential equations with boundary conditions, Stochastics, 1981, 5(4), 225–309 http://dx.doi.org/10.1080/17442508108833184
  • [5] Constantini C., Pacchiarotti B., Sartoretto F., Numerical approximation for functionals of reflecting diffusion processes, SIAM J. Appl. Math., 1998, 58(1), 73–102 http://dx.doi.org/10.1137/S0036139995291040
  • [6] Ding D., Zhang Y.Y., A splitting-step algorithm for reflected stochastic differential equations in ℝ +1, Comput. Math. Appl., 2008, 55(11), 2413–2425 http://dx.doi.org/10.1016/j.camwa.2007.08.043
  • [7] Karatzas I., Shreve S.E., Brownian Motion and Stochastic Calculus, Grad. Texts in Math., 113, Springer, New York, 1988
  • [8] Kloeden P.E., Platen E., Numerical Solution of Stochastic Differential Equations, Appl. Math. (N. Y.), Springer, Berlin, 1992
  • [9] Lépingle D., Euler scheme for reflected stochastic differential equations, Math. Comput. Simulation, 1995, 38(1–3), 119–126 http://dx.doi.org/10.1016/0378-4754(93)E0074-F
  • [10] Lions P.-L., Sznitman A.-S., Stochastic differential equations with reflecting boundary conditions, Comm. Pure Appl. Math., 1984, 37(4), 511–537 http://dx.doi.org/10.1002/cpa.3160370408
  • [11] Maticiuc L., Răşcanu A., Backward stochastic generalized variational inequality, In: Applied Analysis and Differential Equations, Iaşi, September 4–9, 2006, World Scientific, Hackensack, 2007, 217–226 http://dx.doi.org/10.1142/9789812708229_0018
  • [12] Maticiuc L., Răşcanu A., A stochastic approach to a multivalued Dirichlet-Neumann problem, Stochastic Process. Appl., 2010, 120(6), 777–800 http://dx.doi.org/10.1016/j.spa.2010.02.002
  • [13] Menaldi J.-L., Stochastic variational inequality for reflected diffusion, Indiana Univ. Math. J., 1983, 32(5), 733–744 http://dx.doi.org/10.1512/iumj.1983.32.32048
  • [14] Pardoux É., Peng S.G., Adapted solution of a backward stochastic differential equation, Systems Control Lett., 1990, 14(1), 55–61 http://dx.doi.org/10.1016/0167-6911(90)90082-6
  • [15] Pardoux É., Peng S., Backward stochastic differential equations and quasilinear parabolic partial differential equations, In: Stochastic Partial Differential Equations and their Applications, Charlotte, June 6–8, 1991, Lecture Notes in Control and Inform. Sci., 176, Springer, Berlin, 1992, 200–217 http://dx.doi.org/10.1007/BFb0007334
  • [16] Pardoux E., Răşcanu A., Backward stochastic differential equations with subdifferential operator and related variational inequalities, Stochastic Process. Appl., 1998, 76(2), 191–215 http://dx.doi.org/10.1016/S0304-4149(98)00030-1
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  • [22] SŁominski L., On approximation of solutions of multidimensional SDEs with reflecting boundary conditions, Stochastic Process. Appl., 1994, 50(2), 179–219
  • [23] Zhang J., Some Fine Properties of Backward Stochastic Differential Equations, PhD thesis, Purdue University, 2001

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Bibliografia

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