106 research outputs found
Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise
From Crossref journal articles via Jisc Publications RouterHistory: epub 2024-01-23, issued 2024-01-23Article version: VoRPublication status: PublishedWe consider a numerical approximation for stochastic fractional differential equations driven by integrated multiplicative noise. The fractional derivative is in the Caputo sense with the fractional order α∈(0,1), and the non-linear terms satisfy the global Lipschitz conditions. We first approximate the noise with the piecewise constant function to obtain the regularized stochastic fractional differential equation. By applying Minkowski’s inequality for double integrals, we establish that the error between the exact solution and the solution of the regularized problem has an order of O(Δtα) in the mean square norm, where Δt denotes the step size. To validate our theoretical conclusions, numerical examples are presented, demonstrating the consistency of the numerical results with the established theory
Stability of Analytical and Numerical Solutions for Nonlinear Stochastic Delay Differential Equations with Jumps
This paper is concerned with the stability of analytical and numerical solutions for nonlinear stochastic delay differential equations (SDDEs) with jumps. A sufficient condition for mean-square exponential stability of the exact solution is derived. Then, mean-square stability of the numerical solution is investigated. It is shown that the compensated stochastic θ methods inherit stability property of the exact solution. More precisely, the methods are mean-square stable for any stepsize Δt=τ/m when 1/2≤θ≤1, and they are exponentially mean-square stable if the stepsize Δt∈(0,Δt0) when 0≤θ<1. Finally, some numerical experiments are given to illustrate the theoretical results
Stabilization via delay feedback for highly nonlinear stochastic time-varying delay systems with Markovian switching and Poisson jump
Little work seems to be known about stabilization results of highly nonlinear stochastic time-varying delay systems (STVDSs) with Markovian switching and Poisson jump. This paper is concerned with the stabilization problem for a class of STVDSs with Markovian switching and Poisson jump. The coefficients of such systems do not satisfy the conventional linear growth conditions, but are subject to high nonlinearity. The aim of this paper is to design a delay feedback controller to make an unstable highly nonlinear STVDSs with Markovian switching and Poisson jump H∞-stable and asymptotically stable. Besides, an illustrative example is provided to support the theoretical results
Mini-Workshop: Dynamics of Stochastic Systems and their Approximation
The aim of this workshop was to bring together specialists in the area of stochastic dynamical systems and stochastic numerical analysis to exchange their ideas about the state of the art of approximations of stochastic dynamics. Here approximations are considered in the analytical sense in terms of deriving reduced dynamical systems, which are less complex, as well as in the numerical sense via appropriate simulation methods. The main theme is concerned with the efficient treatment of stochastic dynamical systems via both approaches assuming that ideas and methods from one ansatz may prove beneficial for the other. A particular goal was to systematically identify open problems and challenges in this area
International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts
The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of
Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the
International Conference on Mathematical Analysis and Applications in Science and Engineering –
ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days).
Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering,
industry, and technology, to discuss the development of new mathematical models, theories, and
applications that contribute to the advancement of scientific knowledge and practice. Authors proposed
research in topics including partial and ordinary differential equations, integer and fractional order
equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization,
control, probability, computational mathematics, amongst others.
The conference was designed to maximize the involvement of all participants and will present the state-of-
the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio
Measuring and Modelling the Volatility of Financial Time Series
The thesis studies the measures and models of volatility for financial time series. We address the dependency of volatility on sampling frequency and show that this relationship can be explained by using delay equations for the underlying prices. In addition, a new implied volatility process is proposed to reduce the impact of the price movement. This allows us to improve the forecast accuracy of future volatility via the heterogeneous autoregressive model and random forest algorithm
Conditions for wave trains in spiking neural networks
Spatiotemporal patterns such as traveling waves are frequently observed in
recordings of neural activity. The mechanisms underlying the generation of such
patterns are largely unknown. Previous studies have investigated the existence
and uniqueness of different types of waves or bumps of activity using
neural-field models, phenomenological coarse-grained descriptions of
neural-network dynamics. But it remains unclear how these insights can be
transferred to more biologically realistic networks of spiking neurons, where
individual neurons fire irregularly. Here, we employ mean-field theory to
reduce a microscopic model of leaky integrate-and-fire (LIF) neurons with
distance-dependent connectivity to an effective neural-field model. In contrast
to existing phenomenological descriptions, the dynamics in this neural-field
model depends on the mean and the variance in the synaptic input, both
determining the amplitude and the temporal structure of the resulting effective
coupling kernel. For the neural-field model we employ liner stability analysis
to derive conditions for the existence of spatial and temporal oscillations and
wave trains, that is, temporally and spatially periodic traveling waves. We
first prove that wave trains cannot occur in a single homogeneous population of
neurons, irrespective of the form of distance dependence of the connection
probability. Compatible with the architecture of cortical neural networks, wave
trains emerge in two-population networks of excitatory and inhibitory neurons
as a combination of delay-induced temporal oscillations and spatial
oscillations due to distance-dependent connectivity profiles. Finally, we
demonstrate quantitative agreement between predictions of the analytically
tractable neural-field model and numerical simulations of both networks of
nonlinear rate-based units and networks of LIF neurons.Comment: 36 pages, 8 figures, 4 table
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