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We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is obtained via the uniform integrability of…
It is well known that the weak limit of a suitably scaled continuous-time random walk (CTRW) is the Brownian motion. We investigate the convergence of certain patterned random matrices whose entries are independent CTRWs and their…
In the eighties, A. Connes and E. J. Woods made a connection between hyperfinite von Neumann algebras and Poisson boundaries of time dependent random walks. The present paper explains this connection and gives a detailed proof of two…
Optogenetics is a powerful neuroscience technique for studying how neural circuit manipulation affects behavior. Standard analysis conventions discard information and severely limit the scope of the causal questions that can be probed. To…
We prove existence and uniqueness of a stationary distribution and absolute regularity for nonlinear GARCH and INGARCH models of order (p,q). In contrast to previous work we impose, besides a geometric drift condition, only a…
Classical linear regression is considered for a case when regression parameters depend on the external random environment. The last is described as a continuous time Markov chain with finite state space. Here the expected sojourn times in…
The data processing inequality is central to information theory and motivates the study of monotonic divergences. However, it is not clear operationally we need to consider all such divergences. We establish a simple method for Pinsker…
We study time-reversal symmetry in dynamical systems with finite phase space, with applications to birational maps reduced over finite fields. For a polynomial automorphism with a single family of reversing symmetries, a universal (i.e.,…
We describe a procedure to introduce general dependence structures on a set of random variables. These include order-$q$ moving average-type structures, as well as seasonal, periodic, spatial and spatio-temporal dependences. The invariant…
We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean…
We develop a general estimation and inference procedure for the common parameters in linear panel data regression models with nonparametric two-way specification of unobserved heterogeneity. The procedure takes as input any first-step…
This paper describes new results linking constrained optimization theory and nonlinear contraction analysis. Generalizations of Lagrange parameters are derived based on projecting system dynamics on the tangent space of possibly…
We consider bootstrap inference in predictive (or Granger-causality) regressions when the parameter of interest may lie on the boundary of the parameter space, here defined by means of a smooth inequality constraint. For instance, this…
Standard dynamics models for continuous control make use of feedforward computation to predict the conditional distribution of next state and reward given current state and action using a multivariate Gaussian with a diagonal covariance…
Time series data arising in many applications nowadays are high-dimensional. A large number of parameters describe features of these time series. We propose a novel approach to modeling a high-dimensional time series through several…
We present a constraint-based algorithm for learning causal structures from observational time-series data, in the presence of latent confounders. We assume a discrete-time, stationary structural vector autoregressive process, with both…
We provide new limit theory for functionals of a general class of processes lying at the boundary between stationarity and nonstationarity -- what we term weakly nonstationary processes (WNPs). This includes, as leading examples, fractional…
We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…
This paper analyzes the convergence for a large class of Riemannian stochastic approximation (SA) schemes, which aim at tackling stochastic optimization problems. In particular, the recursions we study use either the exponential map of the…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…