Related papers: Mixing properties of Skellam-GARCH processes
We propose a hybrid model of portfolio credit risk where the dynamics of the underlying latent variables is governed by a one factor GARCH process. The distinctive feature of such processes is that the long-term aggregate return…
In this paper we consider the problem of sampling from the low-temperature exponential random graph model (ERGM). The usual approach is via Markov chain Monte Carlo, but Bhamidi et al. showed that any local Markov chain suffers from an…
Stochastic gradient descent (SGD) is a popular algorithm for minimizing objective functions that arise in machine learning. For constant step-sized SGD, the iterates form a Markov chain on a general state space. Focusing on a class of…
We consider a stochastic model of gene expression in which transcription depends on a multistate promoter, including the famous two-state model and refractory promoters as special cases, and focus on deriving the exact stationary…
We have studied Markov processes on denumerable state space and continuous time. We found that all these processes are connected via gauge transformations. We have used this result before as a method for resolution of equations, included…
We propose a novel method to quantify the clustering behavior in a complex time series and apply it to a high-frequency data of the financial markets. We find that regardless of used data sets, all data exhibits the volatility clustering…
We consider the fluctuations of a time-integrated particle current around an atypical value in a generic stochastic Markov process involving classical particles with two-site interaction and hardcore repulsion on a finite one-dimensional…
We introduce a mltiparameter version of Skellam point process via multiparameter Poisson processes. Its distributional properties are studied in detail. Its compound representation is derived for a particular case. Also, its Riemann…
This paper introduces a unique and valuable research design aimed at analyzing Bitcoin price volatility. To achieve this, a range of models from the Markov Switching-GARCH and Stochastic Autoregressive Volatility (SARV) model classes are…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
In this study, we develop a unified volatility modeling framework that embeds GARCH dynamics directly within recurrent neural networks. We propose two interpretable hybrid architectures, GARCH-GRU and GARCH-LSTM, that integrate the…
Block Gram-Schmidt algorithms serve as essential kernels in many scientific computing applications, but for many commonly used variants, a rigorous treatment of their stability properties remains open. This work provides a comprehensive…
We investigate the evolution of the phase-space distribution function around slightly perturbed stationary states and the process of violent relaxation in the context of the dissipationless collapse of an isolated spherical self-gravitating…
This work constructs a new class of multirate schemes based on the recently developed generalized additive Runge-Kutta (GARK) methods (Sandu and Guenther, 2013). Multirate schemes use different step sizes for different components and for…
A simple phenomenological model of a binary granular mixture is developed and investigated numerically. We attempt to model the experimental system of [1,2] where a horizontally vibrated binary monolayer was found to exhibit a transition…
Volatility clustering and spillovers are key features of real-world financial time series when there are a lot of cross-sectional financial assets. While network analysis helps connect stocks that are 'similar' or 'correlated', which is…
We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that satisfy a multiple mixing condition on a space of functions…
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product…
This paper introduces a novel quantile approach to harness the high-frequency information and improve the daily conditional quantile estimation. Specifically, we model the conditional standard deviation as a realized GARCH model and employ…
We observe the continuous-time Markov Branching Process without high-order moments and allowing Immigration. Limit properties of transition functions and their convergence to invariant measures are investigated. Main mathematical tool is…