Strong convergence rate for multivalued stochastic differential equations via stochastic theta method

Abstract In this paper we study the stochastic theta method for multivalued stochastic differential equations driven by standard Brownian motions and obtain the strong convergence rate of this numerical scheme.

[1]  Exponential ergodicity of non-Lipschitz multivalued stochastic differential equations , 2010, 1104.5106.

[2]  Jiagang Ren,et al.  Support theorem for stochastic variational inequalities , 2010, 1005.3136.

[3]  L. Slominski.  Euler's approximations of solutions of SDEs with reflecting boundary , 2001 .

[4]  Siyan Xu,et al.  A transfer principle for multivalued stochastic differential equations , 2009 .

[5]  Leszek Słomiński.  On approximation of solutions of multidimensional SDE's with reflecting boundary conditions , 1994 .

[6]  The optimal control problem associated with multi-valued stochastic differential equations with jumps , 2013 .

[7]  Haisen Zhang.  Stochastic Theta Method for a Reflected Stochastic Differential Equation , 2014 .

[8]  P. Lions,et al.  Stochastic differential equations with reflecting boundary conditions , 1984 .

[9]  Uniform large deviations for multivalued stochastic differential equations with Poisson jumps , 2011 .

[10]  R. Pettersson.  Projection scheme for stochastic differential equations with convex constraints , 2000 .

[11]  Andrew Storm.  Stochastic differential equations with a convex constraint , 1995 .

[12]  Large Deviations for Multivalued Stochastic Differential Equations , 2010 .

[13]  Desmond J. Higham,et al.  Mean-Square and Asymptotic Stability of the Stochastic Theta Method , 2000, SIAM J. Numer. Anal..

[14]  Jing Wu,et al.  Penalization schemes for multi-valued stochastic differential equations , 2013 .

[15]  Jing Wu,et al.  On regularity of invariant measures of multivalued stochastic differential equations , 2012 .

[16]  Giovanna Nappo,et al.  On the Moments of the Modulus of Continuity of Itô Processes , 2009 .

[17]  Nguyen T. Thao,et al.  Approximating and Simulating Multivalued Stochastic Differential Equations , 2004, Monte Carlo Methods Appl..

[18]  E. Cépa.  Problème de Skorohod multivoque , 1998 .

[19]  Second order Hamilton–Jacobi–Bellman equations with an unbounded operator ☆ , 2012 .

[20]  F. Bernardin.  Multivalued Stochastic Differential Equations: Convergence of a Numerical Scheme , 2003 .

[21]  V. Barbu.  Nonlinear Semigroups and di erential equations in Banach spaces , 1976 .

[22]  Skorohod problem and multivalued stochastic evolution equations in Banach spaces , 2007 .

[23]  Weak Solutions and Optimal Control for Multivalued Stochastic Differential Equations , 2008 .

[24]  Roger Pettersson,et al.  Penalization schemes for reflecting stochastic differential equations , 1997 .

[25]  Hiroshi Tanaka.  Stochastic differential equations with reflecting boundary condition in convex regions , 1979 .

[26]  T. Faniran.  Numerical Solution of Stochastic Differential Equations , 2015 .

[27]  General Large Deviations and Functional Iterated Logarithm Law for Multivalued Stochastic Differential Equations , 2015, 1505.02334.