Related papers: Extended Conditional G-Expectations and Related St…
Time variation of Newtonian gravitational constant, $G$, is studied in the model universe with variable space dimension proposed recently. Using the Lagrangian formulation of these models, we find the effective gravitational constant as a…
This paper investigates the stability of a class of differential systems time-changed by $E_{t}$ which is the inverse of a $\beta$-stable subordinator. In order to explore stability, a time-changed Gronwall's inequality and a generalized…
Given a real valued and time-inhomogeneous martingale diffusion X, we investigate the properties of functions defined by the conditional expectation f(t,X_t)=E[g(X_T)|F_t]. We show that whenever g is monotonic or Lipschitz continuous then…
We consider a financial market in discrete time and study pricing and hedging conditional on the information available up to an arbitrary point in time. In this conditional framework, we determine the structure of arbitrage-free prices.…
This brief gives a set of unified Lyapunov stability conditions to guarantee the predefined-time/finite-time stability of a dynamical systems. The derived Lyapunov theorem for autonomous systems establishes equivalence with existing…
This technical note studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibit predefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-time stable and an upper bound of…
We first give a decomposition for a $T$-invariant sublinear expectation $\mathbb{E}=\sup_{P\in\Theta}\mathrm{E}_P$, and show that each component $\mathbb{E}^{(d)}=\sup_{P\in\Theta^{(d)}}\mathrm{E}_P$ of the decomposition has a finite period…
We consider a continuous-time random walk which is the generalization, by means of the introduction of waiting periods on sites, of the one-dimensional nonhomogeneous random walk with a position-dependent drift known in the mathematical…
The derivation of dynamical laws for general observables (or moments) from the master equation for the probability distribution remains a challenging problem in statistical physics. Here, we present an alternative formulation of the general…
We review the behaviour of the Gibbs' and conditional entropies in deterministic and stochastic systems and continue to a formulation appropriate for a stochastically perturbed system with delayed dynamics. The underlying question driving…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…
This paper introduces assume/guarantee contracts on continuous-time control systems, hereby extending contract theories for discrete systems to certain new model classes and specifications. Contracts are regarded as formal characterizations…
We define a fragment of metric first-order temporal logic formulas that guarantees the finiteness of their table representations. We extend our fragment's definition to cover the temporal dual operators trigger and release and show that our…
This brief pedagogical note re-proves a simple theorem on the convergence, in $L_2$ and in probability, of time averages of non-stationary time series to the mean of expectation values. The basic condition is that the sum of covariances…
We discuss existence and uniqueness of stationary and ergodic nonlinear autoregressive processes when exogenous regressors are incorporated in the dynamic. To this end, we consider the convergence of the backward iterations of dependent…
A generalization of stable and casual stable probability distribution is proposed. The notion of $\go G$-casual stability can be used to introduce discrete analogues of stable distributions on the sent $\mathbb Z$ of integers. In contrary…
While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of…
In this paper, we will investigate the moment exponential stabilization of highly nonlinear hybrid stochastic differential delay equations. A periodically intermittent controller based on discrete time state observations with asynchronous…