Related papers: Approximate Likelihood Construction for Rough Diff…
This paper mainly addresses the optimization of $p$-th moment of $\mathbb{R}^n$-valued random variable. Through an ingenious approximation mechanism, one transforms the maximization problem into a sequence of minimization problems, which…
We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g. exchangeable observational units or features) and contiguous groups, or…
This work focuses on the Laplace approximation for the rough differential equation (RDE) driven by mixed rough path with as . Firstly, based on geometric rough path lifted from mixed fractional Brownian motion (fBm), the Schilder-type large…
We present an approximated maximum likelihood method for the multifractal random walk processes of [E. Bacry et al., Phys. Rev. E 64, 026103 (2001)]. The likelihood is computed using a Laplace approximation and a truncation in the…
In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…
In this paper we study the randomized non-autonomous complete linear differential equation. The diffusion coefficient and the source term in the differential equation are assumed to be stochastic processes and the initial condition is…
Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional…
Given a probability distribution $\mu$ a set $\Lambda (\mu)$ of positive real numbers is introduced, so that $\Lambda (\mu)$ measures the "divisibility" of $\mu$. The basic properties of $\Lambda (\mu)$ are described and examples of…
Subject of this letter is the dynamics of a chain obtained performing the continuous limit of a system of links and beads. In particular, the probability distribution of the relative position between two points of the chain averaged over a…
A probabilistic approach is developed for the exact solution $u$ to a determinist partial differential equation as well as for its associated approximation $u^{(k)}_{h}$ performed by $P_k$ Lagrange finite element. Two limitations motivated…
A composite likelihood is an inference function derived by multiplying a set of likelihood components. This approach provides a flexible framework for drawing inference when the likelihood function of a statistical model is computationally…
We prove well-posedness and rough path stability of a class of linear and semi-linear rough PDE's on $\mathbb{R}^d$ using the variational approach. This includes well-posedness of (possibly degenerate) linear rough PDE's in…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
The theory of rough paths arose from a desire to establish continuity properties of ordinary differential equations involving terms of low regularity. While essentially an analytic theory, its main motivation and applications are in…
In this report, the explicit probability density functions of the random Euclidean distances associated with equilateral triangles are given, when the two endpoints of a link are randomly distributed in 1) the same triangle, 2) two adjacent…
A general piecewise (including pointwise) probability distribution with space-saving notation and its hierarchical particular cases are considered. The explicit closed-form normalization, expectation, and variance formulas along with the…
In this paper we address the complexity of solving linear programming problems with a set of differential equations that converge to a fixed point that represents the optimal solution. Assuming a probabilistic model, where the inputs are…
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
A method to approximate continuous multi-dimensional probability density functions (PDFs) using their projections and correlations is described. The method is particularly useful for event classification when estimates of systematic…