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Lossy data compression lies at the heart of modern communication and storage systems. Shannon's rate-distortion theory provides the fundamental limit on how much a source can be compressed at a given fidelity, but it assumes infinitely long…
We study a decentralized variant of stochastic approximation, a data-driven approach for finding the root of an operator under noisy measurements. A network of agents, each with its own operator and data observations, cooperatively find the…
This work focuses on time-inhomogeneous Markov chains with two time scales. Our motivations stem from applications in reliability and dependability, queueing networks, financial engineering and manufacturing systems, where two-time-scale…
This paper studies a variant of the rate-distortion problem motivated by task-oriented semantic communication and distributed learning systems, where $M$ correlated sources are independently encoded for a central decoder. The decoder has…
We consider finite blocklength lossy compression of information sources whose components are independent but non-identically distributed. Crucially, Gaussian sources with memory and quadratic distortion can be cast in this form. We show…
A two-terminal interactive function computation problem with alternating messages is studied within the framework of distributed block source coding theory. For any finite number of messages, a single-letter characterization of the…
In the paper the rescaled occupation time fluctuation process of a certain empirical system is investigated. The system consists of particles evolving independently according to \alpha-stable motion in R^d, \alpha<d<2\alpha. The particles…
We prove central limit theorems, Berry-Esseen type theorems, almost sure invariance principles, large deviations and Livsic type regularity for partial sums of the form $S_n=\sum_{j=0}^{n-1}f_j(...,X_{j-1},X_j,X_{j+1},...)$, where $(X_j)$…
In this paper we study the functional central limit theorem for stationary Markov chains with self-adjoint operator and general state space. We investigate the case when the variance of the partial sum is not asymptotically linear in n; and…
In this work, we study fixed point algorithms for finding a zero in the sum of $n\geq 2$ maximally monotone operators by using their resolvents. More precisely, we consider the class of such algorithms where each resolvent is evaluated only…
This paper studies the minimum achievable source coding rate as a function of blocklength $n$ and probability $\epsilon$ that the distortion exceeds a given level $d$. Tight general achievability and converse bounds are derived that hold at…
The partial sum of the states of a Markov chain or more generally a Markov source is asymptotically normally distributed under suitable conditions. One of these conditions is that the variance is unbounded. A simple combinatorial…
A functional central limit theorem is established for weighted occupancy processes of the Karlin model. The weighted occupancy processes take the form of, with $D_{n,j}$ denoting the number of urns with $j$-balls after the first $n$…
In the present study, we investigate the full counting statistics in a two-terminal Aharonov-Bohm interferometer embedded with an interacting quantum dot. We introduce a novel saddle-point solution for a cumulant-generating function, which…
In this work we connect the theory of Dirichlet forms and direct stochastic calculus to obtain strong existence and pathwise uniqueness for Brownian motion that is perturbed by a series of constant multiples of local times at a sequence of…
It is proved that the limit of the normalized rate-distortion functions of block independent approximations of an irreducible, aperiodic Markoff chain is independent of the initial distribution of the Markoff chain and thus, is also equal…
Let $\Phi_n$ be an i.i.d. sequence of Lipschitz mappings of $\R^d$. We study the Markov chain $\{X_n^x\}_{n=0}^\infty$ on $\R^d$ defined by the recursion $X_n^x = \Phi_n(X^x_{n-1})$, $n\in\N$, $X_0^x=x\in\R^d$. We assume that…
We present the problem of two-terminal source coding with Common Sum Reconstruction (CSR). Consider two terminals, each with access to one of two correlated sources. Both terminals want to reconstruct the sum of the two sources under some…
We consider the Fleming--Viot particle system associated with a continuous-time Markov chain in a finite space. Assuming irreducibility, it is known that the particle system possesses a unique stationary distribution, under which its…
Numerical differentiation of a function, contaminated with noise, over the unit interval $[0,1] \subset \mathbb{R}$ by inverting the simple integration operator $J:L^2([0,1]) \to L^2([0,1])$ defined as $[Jx](s):=\int_0^s x(t) dt$ is…