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In this paper, we consider Caputo type fractional stochastic time-delay system with permutable matrices. We derive stochastic analogue of variation of constants formula via a newly defined delayed Mittag-Leffer type matrix function. Thus,…
Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
We study the convergence of stochastic fixed point iterations in the consistent case (in the sense of Butnariu and Fl{\aa}m (1995)) in several different settings, under decreasingly restrictive regularity assumptions of the fixed point…
In this paper, we propose a chance constrained stochastic model predictive control scheme for reference tracking of distributed linear time-invariant systems with additive stochastic uncertainty. The chance constraints are reformulated…
The challenging problem of conducting fully Bayesian inference for the reaction rate constants governing stochastic kinetic models (SKMs) is considered. Given the challenges underlying this problem, the Markov jump process representation is…
In this paper, the weak convergence about the discretization error of stochastic iterated integrals in the Skorohod sense are studied, while the integrands and integrators of iterated integrals are supposed to be semimartingales with jumps.…
Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze the states of such systems and their bifurcation structure on…
In this paper, we consider multistopping problems for finite discrete time sequences $X_1,...,X_n$. $m$-stops are allowed and the aim is to maximize the expected value of the best of these $m$ stops. The random variables are neither assumed…
Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the…
We study a class of infinite-horizon impulse control problems with execution delay in discrete time. Using probabilistic methods, particularly the notion of the Snell envelope of processes, we construct an optimal strategy among all…
In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach…
We prove a moderate deviation principle for the continuous time interpolation of discrete time recursive stochastic processes. The methods of proof are somewhat different from the corresponding large deviation result, and in particular the…
In this paper we estimate the expected error of a stochastic approximation algorithm where the maximum of a function is found using finite differences of a stochastic representation of that function. An error estimate of $O(n^{-1/5})$ for…
The asymptotic pseudo-trajectory approach to stochastic approximation of Benaim, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field. The asynchronicity of the process is incorporated into…
We obtain an asymptotic H\"older estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized…
An analytical method is advanced for constructing interpolation formulae for complicated problems of statistical mechanics, in which just a few terms of asymptotic expansions are available. The method is based on the self-similar…
This work introduces a stochastic model predictive control scheme for dynamic chance constraints. We consider linear discrete-time systems affected by unbounded additive stochastic disturbance. To synthesize an optimal controller, we solve…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
The usual explicit finite-difference method of solving partial differential equations is limited in stability because it approximates the exact amplification factor by power-series. By adapting the same exponential-splitting method of…