Stochastic Approximation And Adaptive Algorithms For Non Autonomous Differential Equations
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Author | : Amber Catherine Griffiths |
Publisher | : |
Total Pages | : |
Release | : 2014 |
Genre | : Differential equations |
ISBN | : |
Download Stochastic Approximation and Adaptive Algorithms for Non-autonomous Differential Equations Book in PDF, Epub and Kindle
Author | : Albert Benveniste |
Publisher | : Springer |
Total Pages | : 392 |
Release | : 1990 |
Genre | : Mathematics |
ISBN | : |
Download Adaptive Algorithms and Stochastic Approximations Book in PDF, Epub and Kindle
Author | : |
Publisher | : |
Total Pages | : 17 |
Release | : 2000 |
Genre | : |
ISBN | : 9789171706447 |
Download Weak Approximation of Itô Stochastic Differential Equations and Related Adaptive Algorithms Book in PDF, Epub and Kindle
Author | : Quan Yuan |
Publisher | : |
Total Pages | : 136 |
Release | : 2015 |
Genre | : Applied mathematics |
ISBN | : |
Download Stochastic Approximation Algorithms with Applications to Particle Swarm Optimization, Adaptive Optimization, and Consensus Book in PDF, Epub and Kindle
(2) The agents compute and communicate at random times. (3) The regime-switching process is modeled as a discrete-time Markov chain with a finite state space. (4) The functions involved are allowed to vary with respect to time hence nonstationarity can be handled. (5) Multi-scale formulation enriches the applicability of the algorithms. In the setup, the switching process contains a rate parameter $\e> 0$ in the transition probability matrix that characterizes how frequently the topology switches. The algorithm uses a step-size $\mu$ that defines how fast the network states are updated. Depending on their relative values, three distinct scenarios emerge. Under suitable conditions, it is shown that a continuous-time interpolation of the iterates converges weakly to a system of randomly switching ordinary differential equations modulated by a continuous-time Markov chain, or to a system of differential equations (an average with respect to certain measure). In addition, a scaled sequence of tracking errors converges to a witching diffusion or a diffusion. Simulation results are presented to demonstrate these findings.
Author | : Kyoung-Sook Moon |
Publisher | : |
Total Pages | : 26 |
Release | : 2003 |
Genre | : |
ISBN | : 9789172835535 |
Download Adaptive Algorithms for Deterministic and Stochastic Differential Equations Book in PDF, Epub and Kindle
Author | : Harold Kushner |
Publisher | : Springer |
Total Pages | : 0 |
Release | : 2010-11-24 |
Genre | : Mathematics |
ISBN | : 9781441918475 |
Download Stochastic Approximation and Recursive Algorithms and Applications Book in PDF, Epub and Kindle
This book presents a thorough development of the modern theory of stochastic approximation or recursive stochastic algorithms for both constrained and unconstrained problems. This second edition is a thorough revision, although the main features and structure remain unchanged. It contains many additional applications and results as well as more detailed discussion.
Author | : Albert Benveniste |
Publisher | : |
Total Pages | : 0 |
Release | : 1990 |
Genre | : Algorithms |
ISBN | : |
Download Stochastic Approximations and Adaptive Algorithms Book in PDF, Epub and Kindle
Author | : Harold Joseph Kushner |
Publisher | : |
Total Pages | : 27 |
Release | : 1982 |
Genre | : Approximation theory |
ISBN | : |
Download An Invariant Measure Approach to the Convergence of Stochastic Approximations with State Dependent Noise Book in PDF, Epub and Kindle
A new method is presented for quickly getting the ordinary differential equation associated with the asymptotic properties of a stochastic approximation (or the projected algorithm for the constrained problem). Either a(n) yields 0, or a(n) can be constant, in which case the analysis is on the sequence obtained when a yields 0.) The method basically requires that the stochastic approximation be Markov with a Feller transition function, but little else. The simplest result requires that if X sub n is equivalent to x, the corresponding noise process have a unique invariant measure; but the 'non-unique' case can also be treated. No mixing condition is required, nor the construction of averaged test functions, and f(., .) need not be continuous. For the class of sequences treated, the conditions seem easier to verify than for other methods. There are extensions to the non-Markov case. Two examples illustrate the power and ease of use of the approach. Aside from the advantages of the method in treating standard problems, it seems to be particularly useful for handling the type of iterative algorithms which arise in adaptive communication theory, where the dynamics are often discontinuous and the 'noise' is often state dependent due to the effects of feedback.
Author | : Erik von Schwerin |
Publisher | : |
Total Pages | : 16 |
Release | : 2005 |
Genre | : |
ISBN | : 9789172839595 |
Download Convergence Rates of Adaptive Algorithms for Stochastic and Partial Differential Equations Book in PDF, Epub and Kindle
Author | : Kyoung-Sook Moon |
Publisher | : |
Total Pages | : 15 |
Release | : 2001 |
Genre | : |
ISBN | : 9789172831964 |
Download Convergence Rates of Adaptive Algorithms for Deterministic and Stochastic Differential Equations Book in PDF, Epub and Kindle