Accession Number:

ADA021159

Title:

General Convergence Results for Stochastic Approximations Via Weak Convergence Theory,

Descriptive Note:

Corporate Author:

BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS

Personal Author(s):

• Kushner,Harold J.

Report Date:

1976-02-01

Pagination or Media Count:

26.0

Abstract:

Using results in the theory of weak convergence of measures and in stability theory for ordinary differential equations, we prove some general convergence theorems for the sequences of random variables which are generated by algorithms of the stochastic approximation type. Such algorithms are used when one wishes to locate, via a recursive Monte-Carlo method, a minimum of a function, under handicap of noisy data. Algorithms for both constrained and unconstrained optimization problems will be considered, and for rather general noise processes. Author

Descriptors:

• *STOCHASTIC PROCESSES
• *APPROXIMATION(MATHEMATICS)
• *ADAPTIVE SYSTEMS
• RANDOM VARIABLES
• PROBABILITY
• GAUSSIAN NOISE
• MONTE CARLO METHOD
• CONVERGENCE
• DIFFERENTIAL EQUATIONS

Subject Categories:

• Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE