Related papers: Stieltjes differential systems with non monotonic …
A \emph{double extrema form} of the calculus of variations is put forward in which only the smallest one of the finite differences is physically meaningful to represent the variational derivatives defined on the discrete points. The most…
We investigate the asymptotic zero distribution of Heine-Stieltjes polynomials - polynomial solutions of a second order differential equations with complex polynomial coefficients. In the case when all zeros of the leading coefficients are…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
We find Stieltjes-type and Jacobi-type continued fractions for some "master polynomials" that enumerate permutations, set partitions or perfect matchings with a large (sometimes infinite) number of simultaneous statistics. Our results…
We discuss a concept of path-dependent SDE with distributional drift with possible jumps. We interpret it via a suitable martingale problem, for which we provide existence and uniqueness. The corresponding solutions are expected to be…
In this paper we study differentiability properties of the map $T\mapsto\phi(T)$, where $\phi$ is a given function in the disk-algebra and $T$ ranges over the set of contractions on Hilbert space. We obtain sharp conditions (in terms of…
To generalise evolution families we consider systems of contractions $\{\varphi(u, v)\}_{(u, v) \in E}$ defined on the edges of a graph $\mathcal{G} = (\Omega, E)$. In this setup the Markov property, or \emph{divisibility}, can be modelled…
We consider a stochastic flow on $\mathds{R}$ generated by an SDE with its drift being a function of bounded variation. We show that the flow is differentiable with respect to the initial conditions. Asymptotic properties of the flow are…
The connection between derivatives of $L(s,f)$ for periodic arithmetical functions $f$ at $s=1$ and generalized Stieltjes constants has been noted earlier. In this paper, we utilize this link to throw light on the arithmetic nature of…
We explain how It\^o Stochastic Differential Equations (SDEs) on manifolds may be defined using 2-jets of smooth functions. We show how this relationship can be interpreted in terms of a convergent numerical scheme. We show how jets can be…
Understanding, predicting, and controlling physical processes often relies on the analysis of the dynamics of partial differential equations (PDEs). In this context, the present study offers an in-depth investigation into the nonlinear…
In this paper we prove pointwise and distributional Fourier transform inversion theorems for functions on the real line that are locally of bounded variation, while in a neighbourhood of infinity are Lebesgue integrable or have polynomial…
In this paper we present some applications of the Stieltjes constants including, for example, new derivations of Binet's formulae for the log gamma function and the evaluation of some integrals related to the Barnes multiple gamma…
Realised pay-offs for discretisation-invariant swaps are those which satisfy a restricted `aggregation property' of Neuberger [2012] for twice continuously differentiable deterministic functions of a multivariate martingale. They are…
We show that the generalised Stieltjes constants may be represented by infinite series involving logarithmic terms. Some relations involving the derivatives of the Hurwitz zeta function are also investigated
Integrating with respect to functions which are constant on intervals whose bounds are discontinuity points (of those functions) is frequent in many branches of Mathematics, specially in stochastic processes. For such functions and alike…
We give a continued-fraction characterization of Stieltjes moment sequences for which there exists a representing measure with support in $[\xi, \infty)$. The proof is elementary.
We develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category.…
We present a new asymptotic formula for the Stieltjes constants which is both simpler and more accurate than several others published in the literature (see e.g. \cite{Fekih-Ahmed}, \cite{Knessl Coffey}, \cite{Paris}). More importantly, it…
We consider a diffusion equation in $\mathbb{R}^d$ with drift equal to the gradient of a homogeneous potential of degree $1+\gamma$, with $0<\gamma<1$, and local variance equal to $\varepsilon^2$ with $\varepsilon\to 0$. The associated…