Related papers: Characteristic functions of measures on geometric …
In mathematical finance and other applications of stochastic processes, it is frequently the case that the characteristic function may be known but explicit forms for density functions are not available. The simulation of any distribution…
We propose a symbolic execution method for programs that can draw random samples. In contrast to existing work, our method can verify randomized programs with unknown inputs and can prove probabilistic properties that universally quantify…
We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…
We investigate some topological properties of random geometric complexes and random geometric graphs on Riemannian manifolds in the thermodynamic limit. In particular, for random geometric complexes we prove that the normalized counting…
For a graph consisting of parallel connected subgraphs we express the characteristic function of the boundary value problem with generalized Neumann conditions at both joining points via characteristic functions of different boundary…
In this paper, we establish moment and Bernstein-type inequalities for additive functionals of geometrically ergodic Markov chains. These inequalities extend the corresponding inequalities for independent random variables. Our conditions…
Path signatures have been proposed as a powerful representation of paths that efficiently captures the path's analytic and geometric characteristics, having useful algebraic properties including fast concatenation of paths through tensor…
The minimality of the penalization function associated with a convex risk measure is analyzed in this paper. First, in a general static framework, we provide necessary and sufficient conditions for a penalty function defined in a convex and…
We give a new characterization of the space of functions of bounded variation in terms of a pointwise inequality connected to the maximal function of a measure. The characterization is new even in Euclidean spaces and it holds also in…
Conventional quantum mechanics describes a pre- and post-selected system in terms of virtual (Feynman) paths via which the final state can be reached. In the absence of probabilities, a weak measurement (WM) determines the probability…
Suppose an interval is put on a horizontal line with random roughness. With probability one it is supported at two points, one from the left, and another from the right from its center. We compute probability distribution of support points…
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…
A function of the empirical characteristic function,exists for the stable distribution, which leads to a linear regression and can be used to estimate the parameters. Two approaches are often used, one to find optimal values of t, but these…
This paper proposes a methodology to estimate characteristic functions of stochastic differential equations that are defined over polynomials and driven by L\'evy noise. For such systems, the time evolution of the characteristic function is…
Motivated by a result on weak Markov dilations, we define a notion of characteristic function for ergodic and coisometric row contractions with a one-dimensional invariant subspace for the adjoints. This extends a definition given by G.…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
We consider a class of non-homogeneous Markov chains, that contains many natural examples. Next, using martingale methods, we establish some deviation and moment inequalities for separately Lipschitz functions of such a chain, under moment…
In this paper, we propose a flexible notion of characteristic functions defined on graph vertices to describe the distribution of vertex features at multiple scales. We introduce FEATHER, a computationally efficient algorithm to calculate a…
Geometric quantiles are popular location functionals to build rank-based statistical procedures in multivariate settings. They are obtained through the minimization of a non-smooth convex objective function. As a result, the singularity of…
We propose an estimator for the mean of random variables in separable real Banach spaces using the empirical characteristic function. Assuming that the covariance operator of the random variable is bounded in a precise sense, we show that…