Stochastic differential equations (SDEs) and random processes form a central framework for modelling systems influenced by inherent uncertainties. These mathematical constructs are used to rigorously ...

Probabilists are often facing the task to determine the asymptotic behavior of a given sequence of random variables, more precisely, to prove its convergence (in a suitable sense) to a limiting ...

Random walks serve as fundamental models in the study of stochastic processes, simulating phenomena ranging from molecular diffusion to queuing networks and financial systems. Their inherent ...

Many dynamic processes can be described mathematically with the aid of stochastic partial differential equations. Scientists have found a new method which helps to solve a certain class of such ...

In this paper we prove large deviations results for partial sums constructed from the solution to a stochastic recurrence equation. We assume Kesten's condition [Acta Math. 131 (1973) 207—248] under ...