Numerical solution of stochastic differential equations

Technical Report · Thu Aug 01 04:00:00 EDT 1985

OSTI ID:6515199

Chang, C C

We present numerical methods of high order accuracy for solving stochastic differential equations with constant diffusion coefficients. Our analysis is performed in the L/sub 2/ norm, which has the advantage of exhibiting the non-anticipating property of stochastic differential equations. For the scalar case, a second order method of Runge-Kutta type is derived, and in the case of a system, a similar method of order 1-1/2 is presented. By a method of Runge-Kutta type, we mean a one-step method where one needs only to evaluate the function involved at several different points. For the case of a system, we also present a method of Taylor series type, in which the derivatives of the function involved appear explicitly. The analysis of this method in turn leads us to conjecture that the method of order 1-1/2 mentioned above and another simpler method of Runge-Kutta type have a second order accuracy in a weak sense. Finally, variance reduction techniques for evaluating the expectations of functionals of the solution are discussed, and numerical examples are presented.

• Research Organization: Lawrence Berkeley Lab., CA (USA)
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 6515199
• Report Number(s): LBL-20290; ON: DE86002875
• Country of Publication: United States
• Language: English

Related Subjects

658000* -- Mathematical Physics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
EQUATIONS
ITERATIVE METHODS
MATHEMATICS
NUMERICAL ANALYSIS
NUMERICAL SOLUTION
RUNGE-KUTTA METHOD
SERIES EXPANSION
STOCHASTIC PROCESSES