Correlation and moment properties relating numerical integration and stochastic integrals

Technical Report · Thu Apr 01 04:00:00 EST 1982

OSTI ID:5221694

Richardson, J M; Rowland, J R

Correlation between the input noise and system dynamics is shown to be a unifying concept in the digital simulation of nonlinear stochastic systems. More specifically, in order to obtain a unique output time response, this correlation must be provided in addition to the nonliear system dynamic equations, initial conditions, and inputs. Based on first and second moment properties, it is shown that no correlation is present for the Ito stochastic integral, which corresponds to multi-step numerical integration formulas. In the same context, a nonzero correlation is obtained with the Stratonovich stochastic integral and with corresponding single-step (Runge-Kutta) numerical integration formulas. Digitally, this correlation is introduced by the repeated use of each noise increment in the evaluation of the integral. Numerical examples include an optimal nonlinear filter and an air pollution concentration model.

• Research Organization: Sandia National Labs., Albuquerque, NM (USA)
• DOE Contract Number: AC04-76DP00789
• OSTI ID: 5221694
• Report Number(s): SAND-81-1944; ON: DE82016088
• 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
COMPUTER CALCULATIONS
COMPUTERIZED SIMULATION
EQUATIONS
INTEGRAL EQUATIONS
ITERATIVE METHODS
NOISE
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
RUNGE-KUTTA METHOD
SIMULATION
STOCHASTIC PROCESSES