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Section B

Semi-discrete approximations for stochastic differential equations and applications

Pages 780-794 | Received 10 Feb 2011, Accepted 12 Jan 2012, Published online: 23 Feb 2012

References

  • Alfonsi , A. 2005 . On the discretization schemes for the CIR (and Bessel squared) processes . Monte Carlo Methods Appl. , 11 ( 4 ) : 355 – 384 .
  • Assing , S. and Manthey , R. 1995 . The behavior of solutions of stochastic differential inequalities . Probab. Theory Related Fields , 103 ( 4 ) : 493 – 514 .
  • Barlow , M. and Perkins , E. 1984 . One-dimensional stochastic differential equations involving a singular increasing process . Stochastics , 12 : 229 – 249 .
  • Carmona , R. and Tehranchi , M. 2006 . Interest Rate Models: An Infinite Dimensional Stochastic Analysis Perspective , Berlin : Springer-Verlag .
  • Cherny , A. and Engelbert , H. 2005 . Singular Stochastic Differential Equations , Berlin : Springer-Verlag .
  • Cox , J. C. , Ingersoll , J. E. and Ross , S. A. 1985 . A theory of the term structure of interest rates . Econometrica , 53 : 385 – 407 .
  • Higham , D. and Kloeden , P. 2005 . Numerical Methods for Nonlinear Stochastic Differential Equations with Jumps . Numer. Math. , 101 ( 1 ) : 101 – 119 .
  • Higham , D. and Mao , X. 2005 . Convergence of Monte Carlo simulations involving the mean-reverting square root process . J. Comput. Finance , 8 : 35 – 61 .
  • Higham , D. , Mao , X. and Stuart , A. 2002 . Strong convergence of Euler-type methods for nonlinear stochastic differential equations . SIAM J. Numer. Anal. , 40 : 1041 – 1063 .
  • Karatzas , I. and Shreve , S. 1991 . Brownian Motion and Stochastic Calculus , New York : Springer .
  • Kloeden , P. and Platen , E. 1999 . Numerical Solution of Stochastic Differential Equations , Berlin : Springer-Verlag .
  • Lepeltier , J. P. and San Martin , J. 1997 . Backward stochastic differential equations with continuous coefficient . Statist. Probab. Lett. , 32 : 425 – 430 .
  • Milstein , G. and Tretyakov , M. 2004 . Stochastic Numerics for Mathematical Physics , Berlin : Springer-Verlag .
  • Moro , E. and Schurz , H. 2007 . Boundary preserving semi-analytic numerical algorithms for stochastic differential equations . SIAM J. Sci. Comput. , 29 : 1525 – 1549 .
  • Platen , E. and Bruti-Liberati , N. 2010 . Numerical Solution of Stochastic Differential Equations with Jumps in Finance , Berlin : Springer-Verlag .
  • Schurz , H. 1996 . Numerical regularization for SDEs: Construction of nonnegative solutions . Dynam. Systems Appl. , 5 : 323 – 352 .

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