相关论文: A Note on Maximum and Minimum Stability of Certain…

We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…

This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the…

The exponential stability, in both mean square and almost sure senses, for energy solutions to a class of nonlinear and non-autonomous stochastic PDEs with finite memory is investigated. Various criteria for stability are obtained. An…

We study the extremes of a sequence of random variables $(R_n)$ defined by the recurrence $R_n=M_nR_{n-1}+q$, $n\ge1$, where $R_0$ is arbitrary, $(M_n)$ are iid copies of a non--degenerate random variable $M$, $0\le M\le1$, and $q>0$ is a…

Given $n$ independent random marked $d$-vectors (points) $X_i$ distributed with a common density, define the measure $\nu_n=\sum_i\xi_i$, where $\xi_i$ is a measure (not necessarily a point measure) which stabilizes; this means that $\xi_i$…

The stability of random variables can be generalized in any convex cone. In this case the principal results about the LePage representation and the domains of attraction are analogous but different to those well known for general Banach…

We study the stability of randomized Taylor schemes for ODEs. We consider three notions of probabilistic stability: asymptotic stability, mean-square stability, and stability in probability. We prove fundamental properties of the…

We find the exponential exact two-terms non-asymptotic expression for the maximum and minimum distribution of a non-Gaussian, in general case, random vector.

Consider the general scalar balance law $\partial_t u + \Div f(t, x,u) = F(t,x,u)$ in several space dimensions. The aim of this note is to estimate the dependence of its solutions from the flow $f$ and from the source $F$. To this aim, a…

We consider a nonlinear polynomial regression model in which we wish to test the null hypothesis of structural stability in the regression parameters against the alternative of a break at an unknown time. We derive the extreme value…

Two old conjectures from problem sections, one of which from SIAM Review, concern the question of finding distributions that maximize P(Sn <= t), where Sn is the sum of i.i.d. random variables X1, ..., Xn on the interval [0,1], satisfying…

We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…

We study p-adic counterparts of stable distributions, that is limit distributions for sequences of normalized sums of independent identically distributed p-adic-valued random variables. In contrast to the classical case, non-degenerate…

In statistical physics lately a specific kind of average, called the q-expectation value, has been extensively used in the context of q-generalized statistics dealing with distributions following power-laws. In this context q-expectation…

Let $\mathbf{X}(n) \in \mathbb{R}^d$ be a sequence of random vectors, where $n\in\mathbb{N}$ and $d = d(n)$. Under certain weakly dependence conditions, we prove that the distribution of the maximal component of $\mathbf{X}$ and the…

We give an approach to exponential stability within the framework of evolutionary equations due to [R. Picard. A structural observation for linear material laws in classical mathematical physics. Math. Methods Appl. Sci.,…

The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the…

For a sequence $\{X_{n}, \, n \geqslant 1 \}$ of random variables satisfying $\mathbb{E} \lvert X_{n} \rvert < \infty$ for all $n \geqslant 1$, a maximal inequality is established, and used to obtain strong law of large numbers for…

Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied…

Let $E$ be a space of observables in a sequence of trials $\xi_n$ and define $m_n$ to be the empirical distributions of the outcomes. We discuss the almost sure convergence of the sequence $m_n$ in terms of the $\psi$-weak topology of…