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Using Foster-Lyapunov techniques we establish new conditions on non-extinction, non-explosion, coming down from infinity and staying infinite, respectively, for the general continuous-state nonlinear branching processes introduced in Li et…
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…
We analyze here different forms of fractional relaxation equations of order {\nu}\in(0,1) and we derive their solutions both in analytical and in probabilistic forms. In particular we show that these solutions can be expressed as crossing…
Random walks in random scenery are processes defined by $Z_n:=\sum_{k=1}^n\xi_{X_1+...+X_k}$, where $(X_k,k\ge 1)$ and $(\xi_y,y\in{\mathbb Z}^d)$ are two independent sequences of i.i.d. random variables with values in ${\mathbb Z}^d$ and…
Finite dimensional (FD) models, i.e., deterministic functions of time/space and finite sets of random variables, are constructed for target vector-valued random processes/fields. They are required to have two properties. First, standard…
Consider a one-dimensional exclusion process with finite-range translation-invariant jump rates with non-zero drift. Let the process be stationary with product Bernoulli invariant distribution at density \rho. Place a second class particle…
(i) Uncountably many synchronized reflected Brownian motions can hit the boundary of a $C^2$ domain at the same time. (ii) Measures associated to local times of two synchronized reflected Brownian motions are mutually singular until the…
This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated…
Stationary points or derivative zero crossings of a regression function correspond to points where a trend reverses, making their estimation scientifically important. Existing approaches to uncertainty quantification for stationary points…
In this paper we study approximations for boundary crossing probabilities for the moving sums of i.i.d. normal random variables. We propose approximating a discrete time problem with a continuous time problem allowing us to apply developed…
Driven by diverse applications, several recent models impose randomly switching boundary conditions on either a PDE or SDE. The purpose of this paper is to provide tools for calculating statistics of these models and to establish a…
This thesis is devoted to the application of random matrix theory to the study of random surfaces, both discrete and continuous; special emphasis is placed on surface boundaries and the associated boundary conditions in this formalism. In…
Intermediately subcritical branching processes in random environment are at the borderline between two subcritical regimes and exhibit a particularly rich behavior. In this paper, we prove a functional limit theorem for these processes. It…
The relation between continuous functions and random vectors is revealed in the paper that the main meaning is described as, for any given continuous function, there must be a sequence of probability spaces and a sequence of random vectors…
Shape estimation and object reconstruction are common problems in image analysis. Mathematically, viewing objects in the image plane as random sets reduces the problem of shape estimation to inference about sets. Currently existing…
We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in $\mathbb{R}^d$. The dynamics we study here are those of a Markov birth-death process. We prove functional limit…
We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.
Encounter-based models of diffusion provide a probabilistic framework for analyzing the effects of a partially absorbing reactive surface, in which the probability of absorption depends upon the amount of surface-particle contact time.…
The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary…
The study of a machine learning problem is in many ways is difficult to separate from the study of the loss function being used. One avenue of inquiry has been to look at these loss functions in terms of their properties as scoring rules…