Related papers: Pathwise uniqueness of the squared Bessel and CIR …

We consider a two dimensional reflecting random walk on the nonnegative integer quadrant. It is assumed that this reflecting random walk has skip free transitions. We are concerned with its time reversed process assuming that the stationary…

Given a point S and any irreducible algebraic curve C in P^2 (with any type of singularities), we consider the caustic of reflection defined as the Zariski closure of the envelope of the reflected lines from the point S on the curve C. We…

We review and study a one-parameter family of functional transformations, denoted by $(S^{(\beta)})_{\beta\in \R}$, which, in the case $\beta<0$, provides a path realization of bridges associated to the family of diffusion processes…

We exhibit, in the form of some identities in law, some connections between tilted stable subordinators, time-changed by independent Gamma processes and the occupation times of Bessel spiders, or their bridges. These identities in law are…

Dependence of the transient process duration on the initial conditions is considered in one- and two-dimensional systems with discrete time, representing a logistic map and the Eno map, respectively.

We consider a time inhomogeneous Cox-Ingersoll-Ross diffusion with positive jumps. We exploit a branching property to prove existence of a unique strong solution under a restrictive condition on the jump measure. We give Laplace transforms…

The trace of a Markov process is the time changed process of the original process on the support of the Revuz measure used in the time change. In this paper, we will concentrate on the reflecting Brownian motions on certain closed strips.…

When a linear model is adjusted to control for additional explanatory variables the sign of a fitted coefficient may reverse. Here these reversals are studied using coefficients of determination. The resulting theory can be used to…

The uniqueness of the Bohmian particle interpretation of the Kemmer equation, which describes massive spin-0 and spin-1 particles, is discussed. Recently the same problem for spin-1/2 was dealt with by Holland. It appears that the…

The single-particle inclusive differential cross-section for a reaction $a+b\to c+X$ is written as the imaginary part of a correlation function in a for ward scattering amplitude for $a+b\to a+b$ in a modified effective theory. In this…

In the first part of this paper we give a solution for the one-dimensional reflected backward stochastic differential equation (BSDE for short) when the noise is driven by a Brownian motion and an independent Poisson point process. The…

For a class of one-dimensional determinantal point processes including those induced by orthogonal projections with integrable kernels satisfying a growth condition, it is proved that their conditional measures, with respect to the…

We prove pathwise uniqueness for stochastic differential equations driven by non-degenerate symmetric $\alpha$-stable L\'evy processes with values in $\R^d$ having a bounded and $\beta$-H\"older continuous drift term. We assume $\beta > 1 -…

We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…

Let $C$ be an irreducible projective plane curve in the complex projective space ${\mathbb{P}}^2$. The classification of such curves, up to the action of the automorphism group $PGL(3,{\mathbb{C}})$ on ${\mathbb{P}}^2$, is a very difficult…

Constrained Markov processes, such as reflecting diffusions, behave as an unconstrained process in the interior of a domain but upon reaching the boundary are controlled in some way so that they do not leave the closure of the domain. In…

We develop a behavioural theory of reflective sequential algorithms (RSAs), i.e. sequential algorithms that can modify their own behaviour. The theory comprises a set of language-independent postulates defining the class of RSAs, an…

For $\alpha\in (0,1)$, we consider stochastic differential equations driven by one-sided stable processes of order $\alpha$: \[dX_t= \phi(X_{t-})\ dZ_t.\] We prove that pathwise uniqueness holds for this equation under the assumptions that…

We consider exit problems for general L\'evy processes, where the first passage over a threshold is detected either immediately or at an epoch of an independent homogeneous Poisson process. It is shown that the two corresponding one-sided…

Let $X$ be a standard Markov process. We prove that a space inversion property of $X$ implies the existence of a Kelvin transform of $X$-harmonic, excessive and operator-harmonic functions and that the inversion property is inherited by…