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Stochastic Approximation and Recursive Algorithms and Applications
Introduction 1 Review of Continuous Time Models 1.1 Martingales and Martingale Inequalities 1.2 Stochastic Integration 1.3 Stochastic Differential Equations: Diffusions 1.4 Reflected Diffusions 1.5
Stochastic Approximation Algorithms and Applications
Applications and issues application to learning, state dependent noise and queueing applications to signal processing and adaptive control mathematical background convergence with probability one, introduction weak convergence methods for general algorithms applications, proofs of convergence rate of convergence averaging of the iterates distributed/decentralized and asynchronous algorithms.
Hybrid Switching Diffusions: Properties and Applications
and Motivation.- Basic Properties, Recurrence, Ergodicity.- Switching Diffusion.- Recurrence.- Ergodicity.- Numerical Solutions and Approximation.- Numerical Approximation.- Numerical Approximation
Continuous-Time Markov Chains and Applications: A Two-Time-Scale Approach
Prologue and Preliminaries: Introduction and overview- Mathematical preliminaries.- Markovian models.- Two-Time-Scale Markov Chains: Asymptotic Expansions of Solutions for Forward Equations.-
Discrete-Time Markov Chains: Two-Time-Scale Methods and Applications
Prologue and Preliminaries.- Introduction, Overview, and Examples.- Mathematical Preliminaries.- Asymptotic Properties.- Asymptotic Expansions.- Occupation Measures.- Exponential Bounds.- Interim
Continuous-Time Markov Chains and Applications: A Singular Perturbation Approach
Prologue and Preliminaries: Introduction and overview- Mathematical preliminaries. Markovian models.- Singularly perturbed Markov chains: Asymptotic expansion: Irreducible generators. Asymptotic
On extensions of Polyak's averaging approach to stochastic approximation
  • G. Yin
  • Mathematics, Computer Science
  • 1 September 1991
By means of weak convergence methods, it is shown that the multistage algorithms via averaging have asymptotically optimal convergence speed and are efficient procedures.
Option pricing in a regime-switching model using the fast Fourier transform
This paper is concerned with fast Fourier transform (FFT) approach to option valuation, where the underlying asset price is governed by a regime-switching geometric Brownian motion. An FFT method