CATALOG DESCRIPTION: Fundamentals of random variables; mean-squared estimation; limit theorems and convergence; definition of random processes; autocorrelation and stationarity; Gaussian and Poisson ...

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric ...

In the first part of the course, we will start with an introduction to the Gaussian free field (GFF), which is an object which has been at the heart of some recent groundbreaking developments in ...

This is a preview. Log in through your library . Abstract Let ε₁, ...., εn be independent identically distributed Rademacher random variables, that is ℙ{εi = ±1} = 1/2. Let Sn = a₁ε₁ + ... + anεn, ...

In this paper we consider the large homogeneous portfolio (LHP) approximation with a two-factor Gaussian copula and random recovery rate. In addition, we assume that the earlier the default occurs, ...

Random analytic functions are a fundamental object of study in modern complex analysis and probability theory. These functions, often defined through power series with random coefficients, exhibit ...