Digital simulation and modeling of nonlinear stochastic systems

Technical Report · Wed Apr 01 04:00:00 EST 1981

DOI:https://doi.org/10.2172/6489738· OSTI ID:6489738

Richardson, J M; Rowland, J R

Digitally generated solutions of nonlinear stochastic systems are not unique but depend critically on the numerical integration algorithm used. Some theoretical and practical implications of this dependence are examined. The Ito-Stratonovich controversy concerning the solution of nonlinear stochastic systems is shown to be more than a theoretical debate on maintaining Markov properties as opposed to utilizing the computational rules of ordinary calculus. The theoretical arguments give rise to practical considerations in the formation and solution of discrete models from continuous stochastic systems. Well-known numerical integration algorithms are shown not only to provide different solutions for the same stochastic system but also to correspond to different stochastic integral definitions. These correspondences are proved by considering first and second moments of solutions that result from different integration algorithms and then comparing the moments to those arising from various stochastic integral definitions. This algorithm-dependence of solutions is in sharp contrast to the deterministic and linear stochastic cases in which unique solutions are determined by any convergent numerical algorithm. Consequences of the relationship between stochastic system solutions and simulation procedures are presented for a nonlinear filtering example. Monte Carlo simulations and statistical tests are applied to the example to illustrate the determining role which computational procedures play in generating solutions.

• Research Organization: Sandia National Labs., Albuquerque, NM (USA)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC04-76DP00789
• OSTI ID: 6489738
• Report Number(s): SAND-80-2080
• Country of Publication: United States
• Language: English

Related Subjects

657006* -- Theoretical Physics-- Statistical Physics & Thermodynamics-- (-1987)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
COMPUTERIZED SIMULATION
DIFFERENTIAL EQUATIONS
EQUATIONS
MARKOV PROCESS
MATHEMATICAL LOGIC
MATHEMATICAL MODELS
MATHEMATICS
MONTE CARLO METHOD
NONLINEAR PROBLEMS
SIMULATION
STATISTICS
STOCHASTIC PROCESSES