Let X be a d-dimensional diffusion and M the running supremum of its first component. In this paper, we show that for any the density (with respect to the -dimensional Lebesgue measure) of the pair is a weak solution of a Fokker–Planck partial differ…
Let X be a d-dimensional diffusion and M the running supremum of its first component. In this paper, we show that for any the density (with respect to the -dimensional Lebesgue measure) of the pair is a weak solution of a Fokker–Planck partial differ…
We use Stein’s method to establish the rates of normal approximation in terms of the total variation distance for a large class of sums of score functions of samples arising from random events driven by a marked Poisson point process on . As in the stu…
We consider infinitely wide multi-layer perceptrons (MLPs) which are limits of standard deep feed-forward neural networks. We assume that, for each layer, the weights of an MLP are initialized with independent and identically distributed (i.i.d.) sampl…
We consider infinitely wide multi-layer perceptrons (MLPs) which are limits of standard deep feed-forward neural networks. We assume that, for each layer, the weights of an MLP are initialized with independent and identically distributed (i.i.d.) sampl…
We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained, and the position at a given (constant) time of an exponentially tempered Lévy process. The algorithm, based on the increment…
We develop a novel Monte Carlo algorithm for the vector consisting of the supremum, the time at which the supremum is attained, and the position at a given (constant) time of an exponentially tempered Lévy process. The algorithm, based on the increment…
Developed sequential order statistics (DSOS) are very useful in modeling the lifetimes of systems with dependent components, where the failure of one component affects the performance of remaining surviving components. We study some stochastic comparis…
We adapt the classical definition of locally stationary processes in discrete time (see e.g. Dahlhaus, ‘Locally stationary processes’, in Time Series Analysis: Methods and Applications (2012)) to the continuous-time setting and obtain equivalent repres…
This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes, and degree distributions, identifying four regimes: (i) a dense regime, (ii) a …