相关论文: Dynamics of a mean-reverting stochastic volatility…
In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead…
We analyze the relative price change of assets starting from basic supply/demand considerations subject to arbitrary motivations. The resulting stochastic differential equation has coefficients that are functions of supply and demand. We…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
We investigate the behavior of systems of interacting diffusion processes, known as volatility-stabilized market models in the mathematical finance literature, when the number of diffusions tends to infinity. We show that, after an…
In this paper, we study stochastic stability of a dynamical system with shadowing property, which evolves under small random perturbation. We prove that time averages along the pseudo-trajectory converge with respect to stationary measure…
Accurate prediction of financial market volatility is critical for risk management, derivatives pricing, and investment strategy. In this study, we propose a multitude of regime-switching methods to improve the prediction of S&P 500…
In this paper, we introduce a nonresident computer virus model and prove the existence of at least one positive periodic solution. The proposed model is based on a biological approach and is obtained by considering that all rates (rates…
This paper studies the income fluctuation problem with capital income risk (i.e., dispersion in the rate of return to wealth). Wealth returns and labor earnings are allowed to be serially correlated and mutually dependent. Rewards can be…
The role of the equation of state for a perfectly conducting, relativistic magnetized fluid is the main subject of this work. The ideal constant $\Gamma$-law equation of state, commonly adopted in a wide range of astrophysical applications,…
This paper addresses the problem of stabilizing a part of variables for control systems described by stochastic differential equations of the Ito type. The considered problem is related to the asymptotic stability property of invariant sets…
This paper expands traditional stochastic volatility models by allowing for time-varying skewness without imposing it. While dynamic asymmetry may capture the likely direction of future asset returns, it comes at the risk of leading to…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
Resistive switching is one of the foremost candidates for building novel types of non-volatile random access memories. Any practical implementation of such a memory cell calls for a strong miniaturization, at which point fluctuations start…
In this paper we investigate the normal and the large fluctuations of additive functionals associated with a stochastic process under a general non-Poissonian resetting mechanism. Cumulative functionals of regenerative processes are very…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
Genetic switch systems with mutual repression of two transcription factors are studied using deterministic methods (rate equations) and stochastic methods (the master equation and Monte Carlo simulations). These systems exhibit bistability,…
Stochastic resetting, a diffusive process whose amplitude is "reset" to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. We here generalize the resetting step by…
Stochastic unravelings represent a useful tool to describe the dynamics of open quantum systems and standard methods, such as quantum state diffusion (QSD), call for the complete positivity of the open-system dynamics. Here, we present a…
We study persistent random walk with time dependent velocity reversal probabilities and identify a criterion for a non-equilibrium dynamical transition. As a representative example, we consider a power law reversal probability $p(t)\sim…
We study a class of Markov chains that describe reversible stochastic dynamics of a large class of disordered mean field models at low temperatures. Our main purpose is to give a precise relation between the metastable time scales in the…