In contrast to previous research on periodic averaging principles for various types of impulsive stochastic differential equations (ISDEs), we establish an principle without assumptions coefficients and impulses fractional (ISFDEs) excited by Brownian motion (fBm). Under appropriate conditions, demonstrate that the mild solution original equation is approximately equivalent reduced averaged imp...

In this paper, we study the averaging principle for ψ-Capuo fractional stochastic delay differential equations (FSDDEs) with Poisson jumps. Based on calculus, Burkholder-Davis-Gundy’s inequality, Doob’s martingale and Ho¨lder prove that solution of averaged FSDDEs converges to standard in sense Lp. Our result extends some known results literature. Finally, an example simulation is performed sho...

We study diffusion processes and stochastic flows which are time-changed random perturbations of a deterministic flow on manifold. Using non-symmetric Dirichlet forms their convergence in sense close to the Mosco-convergence, we prove that, as is accelerated, process converges law defined different space. This averaging principle also holds at level flows. Our contributions this article include:

In a stochastic environment, two distinct processes, namely nonlinear averaging and non-equilibrium dynamics, influence fitness. We develop methods for decomposing the effects of temporal variation in demography into contributions from nonlinear averaging and non-equilibrium dynamics. We illustrate the approach using Carlina vulgaris, a monocarpic species in which recruitment, growth and surviv...

Effective regularisation during training can mean the difference between success and failure for deep neural networks. Recently, dither has been suggested as alternative to dropout for regularisation during batch-averaged stochastic gradient descent (SGD). In this article, we show that these methods fail without batch averaging and we introduce a new, parallel regularisation method that may be ...

Bayesian averaging over Decision Trees (DTs) allows the class posterior probabilities to be estimated, while the DT models are understandable for domain experts. The use of Markov Chain Monte Carlo (MCMC) technique of stochastic approximation makes the Bayesian DT averaging feasible. In this paper we describe a new Bayesian MCMC technique exploiting a sweeping strategy allowing the posterior di...

Iterative methods that calculate their steps from approximate subgradient directions have proved to be useful for stochastic learning problems over large and streaming data sets. When the objective consists of a loss function plus a nonsmooth regularization term, the solution often lies on a lowdimensional manifold of parameter space along which the regularizer is smooth. (When an l1 regularize...