相关论文: The Logarithmic Asymptotic Phenomenon for Generali…
For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…
The classical Painlev\'e equations are so well known that it may come as a surprise to learn that the asymptotic description of its solutions remains incomplete. The problem lies mainly with the description of families of solutions in the…
Asymptotic properties of Markov Processes, such as steady state probabilities or hazard rate for absorbing states can be efficiently calculated by means of linear algebra even for large-scale problems. This paper discusses the methods for…
A generalization of Hurwitz stable polynomials to real rational functions is considered. We establishe an analogue of the Hurwitz stability criterion for rational functions and introduce a new type of determinants that can be treated as a…
In this paper, we mainly analyze the long-time asymptotics of high-order soliton for the Hirota equation. Two different Riemann-Hilbert representations of Darboux matrix with high-order soliton are given to establish the relationships…
We prove the two-dimensional analogue of the asymptotics for Toeplitz determinants with Fisher-Hartwig singularities, for general real symbols. This formula has applications to random normal matrices with complex spectra: (i) the…
The Gaussian mixed-effects model driven by a stationary integrated Ornstein-Uhlenbeck process has been used for analyzing longitudinal data having an explicit and simple serial-correlation structure in each individual. However, the…
This article introduces mixed double Hurwitz numbers, which interpolate combinatorially between the classical double Hurwitz numbers studied by Okounkov and the monotone double Hurwitz numbers introduced recently by Goulden, Guay-Paquet and…
We consider the Markov renewal equation $F(t) = f(t) + \boldsymbol{\mu}*F(t)$ for vector-valued functions $f,F: \mathbb{R} \to \mathbb{R}^{p}$ and a $p \times p$ matrix $\boldsymbol{\mu}$ of locally finite measures $\mu^{i,j}$ on…
We express some general type of infinite series such as $$ \sum^\infty_{n=1}\frac{F(H_n^{(m)}(z),H_n^{(2m)}(z),\ldots,H_n^{(\ell m)}(z))} {(n+z)^{s_1}(n+1+z)^{s_2}\cdots (n+k-1+z)^{s_k}}, $$ where $F(x_1,\ldots,x_\ell)\in\mathbb…
Using the renewal approach we prove Bernstein-like inequalities for additive functionals of geometrically ergodic Markov chains, thus obtaining counterparts of inequalities for sums of independent random variables. The coefficient in the…
Muttalib-Borodin determinants are generalizations of Hankel determinants and depend on a parameter $\theta>0$. In this paper, we obtain large $n$ asymptotics for $n \times n$ Muttalib-Borodin determinants whose weight possesses an arbitrary…
A modular relation of the form $F(\alpha, w)=F(\beta, iw)$, where $i=\sqrt{-1}$ and $\alpha\beta=1$, is obtained. It involves the generalized digamma function $\psi_w(a)$ which was recently studied by the authors in their work on developing…
We use the Legendre polynomials and the Hermite polynomials as two examples to illustrate a simple and systematic technique on deriving asymptotic formulas for orthogonal polynomials via recurrence relations. Another application of this…
Within the framework of likelihood-based statistical tests for high energy physics measurements, we derive generalized expressions for estimating the statistical significance of discovery using the asymptotic approximations of Wilks and…
It is well known that the Newton method may not converge when the initial guess does not belong to a specific quadratic convergence region. We propose a family of new variants of the Newton method with the potential advantage of having a…
The generalized Hastings-McLeod solutions to the inhomogeneous Painlev\'{e}-II equation arise in multi-critical unitary random matrix ensembles, the chiral two-matrix model for rectangular matrices, non-intersecting squared Bessel paths,…
We employ an adapted version of H\"ormander's asymptotic systems method to show heuristically that the standard good-bad-ugly model admits formal polyhomogeneous asymptotic solutions near null infinity. In a related earlier approach, our…
We introduce completely monotonic functions of order $r>0$ and show that the remainders in asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function give rise to completely monotonic functions of any…
Is studied asymptotic expansion for solution of singularly perturbed equation for Markov random evolution in Rd. The views of regular and singular parts of solution are found.