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Convergence of stochastic approximation via martingale and converse Lyapunov methods
In this paper, we study the almost sure boundedness and the convergence of the stochastic approximation (SA) algorithm. At present, most available...
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Error distribution of the Euler approximation scheme for stochastic Volterra equations
The purpose of this paper is to establish the convergence in distribution of the normalized error in the Euler approximation scheme for stochastic...
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Temporal approximation of stochastic evolution equations with irregular nonlinearities
In this paper, we prove convergence for contractive time discretisation schemes for semi-linear stochastic evolution equations with irregular...
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Approximation to Stochastic Variance Reduced Gradient Langevin Dynamics by Stochastic Delay Differential Equations
We study in this paper weak approximations in Wasserstein-1 distance to stochastic variance reduced gradient Langevin dynamics by stochastic delay...
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An efficient approximation to the stochastic Allen-Cahn equation with random diffusion coefficient field and multiplicative noise
This paper studies the stochastic Allen-Cahn equation involving random diffusion coefficient field and multiplicative force noise. A new...
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Numerical approximation and simulation of the stochastic wave equation on the sphere
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates...
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Some approximation results for mild solutions of stochastic fractional order evolution equations driven by Gaussian noise
We investigate the quality of space approximation of a class of stochastic integral equations of convolution type with Gaussian noise. Such equations...
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Applications to Stochastic Stability
In this chapter, we present applications of some of the Trotter-Kato approximation results from Chapter 3 to stochastic stability problems.
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A dual-based stochastic inexact algorithm for a class of stochastic nonsmooth convex composite problems
In this paper, a dual-based stochastic inexact algorithm is developed to solve a class of stochastic nonsmooth convex problems with underlying...
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Revisiting the ODE Method for Recursive Algorithms: Fast Convergence Using Quasi Stochastic Approximation
Several decades ago, Profs. Sean Meyn and Lei Guo were postdoctoral fellows at ANU, where they shared interest in recursive algorithms. It seems...
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Stochastic enzyme kinetics and the quasi-steady-state reductions: Application of the slow scale linear noise approximation à la Fenichel
The linear noise approximation models the random fluctuations from the mean-field model of a chemical reaction that unfolds near the thermodynamic...
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Diffusive Limit Approximation of Pure-Jump Optimal Stochastic Control Problems
We consider the diffusive limit of a typical pure-jump Markovian control problem as the intensity of the driving Poisson process tends to infinity....
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Sampling-Based Stochastic Linear Programming Methods
In this chapter, we study statistical methods for mean-risk two-stage stochastic linear programs (MR-SLP). We use the theoretical properties of the...
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On Strong Solution to the 2D Stochastic Ericksen–Leslie System: A Ginzburg–Landau Approximation Approach
In this manuscript, we consider a highly nonlinear and constrained stochastic PDEs modelling the dynamics of 2-dimensional nematic liquid crystals...
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An algorithm to estimate parameter in Müntz-Legendre polynomial approximation for the numerical solution of stochastic fractional integro-differential equation
In this paper, we consider the Müntz-Legendre polynomial, which is generated from the fractional basis, and develop a collocation method with the...
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Adaptive Sampling Stochastic Multigradient Algorithm for Stochastic Multiobjective Optimization
In this paper, we propose an adaptive sampling stochastic multigradient algorithm for solving stochastic multiobjective optimization problems....
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Regularized sample average approximation for high-dimensional stochastic optimization under low-rankness
This paper concerns a high-dimensional stochastic programming (SP) problem of minimizing a function of expected cost with a matrix argument. To this...
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Successive Approximation of Neutral Stochastic Partial Integrodifferential Systems with State-Dependent Delay and Poisson Jumps
This study establishes the existence and uniqueness of moderate solutions (MD) of stochastic neutral partial integrodifferential (SNPID) systems with...
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Approximation of the Heat Fluxes Dynamics in the North Atlantic by Stochastic Diffusion Process
AbstractThe observational data for 1979–2018 in the North Atlantic region are analyzed. The dataset contains gridded various information about the...
