Related papers: The logarithmic derivative for point processes wit…
Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
Motivated by a recent surge of interest for Dynkin operators in mathematical physics and by problems in the combinatorial theory of dynamical systems, we propose here a systematic study of logarithmic derivatives in various contexts. In…
We introduce a new setting, the category of $\omega$PAP spaces, for reasoning denotationally about expressive differentiable and probabilistic programming languages. Our semantics is general enough to assign meanings to most practical…
Empirical processes for stationary, causal sequences are considered. We establish empirical central limit theorems for classes of indicators of left half lines, absolutely continuous functions and piecewise differentiable functions. Sample…
In this paper we estimate the rest of the approximation of a stationary process by a martingale in terms of the projections of partial sums. Then, based on this estimate, we obtain almost sure approximation of partial sums by a martingale…
In this paper, we analyse piecewise deterministic Markov processes, as introduced in Davis (1984). Many models in insurance mathematics can be formulated in terms of the general concept of piecewise deterministic Markov processes. In this…
Macdonald processes are probability measures on sequences of partitions defined in terms of nonnegative specializations of the Macdonald symmetric functions and two Macdonald parameters q,t in [0,1). We prove several results about these…
We present an algorithm computing the determinant of an integer matrix A. The algorithm is introspective in the sense that it uses several distinct algorithms that run in a concurrent manner. During the course of the algorithm partial…
We present new algorithms for computing the log-determinant of symmetric, diagonally dominant matrices. Existing algorithms run with cubic complexity with respect to the size of the matrix in the worst case. Our algorithm computes an…
We generalise the martingale-coboundary representation of discrete time stochastic processes to the non-stationary case and to random variables in Orlicz spaces. Related limit theorems (CLT, invariance principle, log log law, probabilities…
Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with…
In this paper, we propose a new concept of derivative with respect to an arbitrary kernel-function. Several properties related to this new operator, like inversion rules, integration by parts, etc. are studied. In particular, we introduce…
A computational technique borrowed from the physical sciences is introduced to obtain accurate closed-form approximations for the transition probability of arbitrary diffusion processes. Within the path integral framework the same technique…
The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations,…
The paper gives a precise asymptotic relation between higher order logarithmic difference and logarithmic derivatives for meromorphic functions with order strictly less then one. This allows us to formulate a useful Wiman-Valiron type…
In the paper we consider some piecewise deterministic Markov process whose continuous component evolves according to semiflows, which are switched at the jump times of a Poisson process. The associated Markov chain describes the states of…
In the present work we show that the joint probability distribution of the eigenvalues can be expressed in terms of a differential operator acting on the distribution of some other matrix quantities. Those quantities might be the diagonal…
Consider a sequence of real-valued functions of a real variable given by a homogeneous linear recursion with differentiable coefficients. We show that if the functions in the sequence are differentiable, then the sequence of derivatives…
We consider the determinantal point process with the confluent hypergeometric kernel. This process is a universal point process in random matrix theory and describes the distribution of eigenvalues of large random Hermitian matrices near…