Related papers: Granger Independent Martingale Processes
The law of the iterated logarithm (LIL) for the time-homogeneous Markov process with a unique invariant measure characterizes the almost sure maximum possible fluctuation of time averages around the ergodic limit. Whether a numerical…
This work focuses on the development of a new class of high-order accurate methods for multirate time integration of systems of ordinary differential equations. Unlike other recent work in this area, the proposed methods support mixed…
A new class of graphical models capturing the dependence structure of events that occur in time is proposed. The graphs represent so-called local independences, meaning that the intensities of certain types of events are independent of some…
We construct a family of self-similar Markov martingales with given marginal distributions. This construction uses the self-similarity and Markov property of a reference process to produce a family of Markov processes that possess the same…
The problem of stochastic deadline scheduling is considered. A constrained Markov decision process model is introduced in which jobs arrive randomly at a service center with stochastic job sizes, rewards, and completion deadlines. The…
We build on a recently introduced geometric interpretation of Markov Decision Processes (MDPs) to analyze classical MDP-solving algorithms: Value Iteration (VI) and Policy Iteration (PI). First, we develop a geometry-based analytical…
Entropy metrics are nonlinear measures to quantify the complexity of time series. Among them, permutation entropy is a common metric due to its robustness and fast computation. Multivariate entropy metrics techniques are needed to analyse…
In this paper we develop a Model Predictive Path Integral (MPPI) control algorithm based on a generalized importance sampling scheme and perform parallel optimization via sampling using a Graphics Processing Unit (GPU). The proposed…
A continuous-time particle system on the real line satisfying the branching property and an exponential integrability condition is called a branching L\'evy process, and its law is characterized by a triplet $(\sigma^2,a,\Lambda)$. We…
In this paper, the weak convergence of additive functionals of processes with locally independent increments and with Markov switching in the scheme of Poisson approximation is proved. For the relative compactness, a method proposed by R.…
In this paper, we introduce a class of processes that contains many natural examples. The interesting feature of such type processes lays on its infinite memory that allows it to record a quite ancient history. Then, using the martingale…
Granger causal modeling is an emerging topic that can uncover Granger causal relationship behind multivariate time series data. In many real-world systems, it is common to encounter a large amount of multivariate time series data collected…
In this paper, we study a multivariate gamma subordinator whose components are independent gamma processes subject to a random time governed by an independent negative binomial process. We derive the explicit expressions for its joint…
Neural Marked Temporal Point Processes (MTPP) are flexible models to capture complex temporal inter-dependencies between labeled events. These models inherently learn two predictive distributions: one for the arrival times of events and…
An interesting family of geometric integrators for Lagrangian systems can be defined using discretizations of the Hamilton's principle of critical action. This family of geometric integrators is called variational integrators. In this…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
A popular and flexible time series model for counts is the generalized integer autoregressive process of order $p$, GINAR($p$). These Markov processes are defined using thinning operators evaluated on past values of the process along with a…
Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typically heterogeneous and often contain multiple known…
We treat the class of universal Markov processes on the d-dimensional Euklidean space which do not depend on random. For these, as well as for several subclasses, we prove criteria whether a function f, defined on the positive half-line,…
The paper introduces and investigates the natural extension to the path-dependent setup of the usual concept of canonical Markov class introduced by Dynkin and which is at the basis of the theory of Markov processes. That extension, indexed…