Let X(t) be the true self-repelling motion (TSRM) constructed by Tóth and Werner (1998) [22], L(t,x) its occupation time density (local time) and H(t):=L(t,X(t)) the height of the local time profile at the actual position of the motion. The joint distribution of (X(t),H(t)) was identified by...

We study the regularity properties of integro-partial differential equations of Hamilton–Jacobi–Bellman type with the terminal condition, which can be interpreted through a stochastic control system, composed of a forward and a backward stochastic differential equation, both driven by a...

We consider random walks in random environments on Zd. Under a transitivity hypothesis that is much weaker than the customary ellipticity condition, and assuming an absolutely continuous invariant measure on the space of the environments, we prove the ergodicity of the annealed process...

We study discrete-time stochastic processes (Xt) on [0,∞) with asymptotically zero mean drifts. Specifically, we consider the critical (Lamperti-type) situation in which the mean drift at x is about c/x. Our focus is the recurrent case (when c is not too large). We give sharp asymptotics for...

For n equidistant observations of a Lévy process at time distance Δn we consider the problem of testing hypotheses on the volatility, the jump measure and its Blumenthal–Getoor index in a non- or semiparametric manner. Asymptotically as n→∞ we allow for both, the high-frequency regime...

We characterize the finite variation property for stationary increment mixed moving averages driven by infinitely divisible random measures. Such processes include fractional and moving average processes driven by Lévy processes, and also their mixtures. We establish two types of zero–one...

The (Ξ,A)-Fleming–Viot process with mutation is a probability-measure-valued process whose moment dual is similar to that of the classical Fleming–Viot process except that Kingman’s coalescent is replaced by the Ξ-coalescent, the coalescent with simultaneous multiple collisions. We first...

Consider the ending time of the tug-of-war without noise in a wedge. There is a critical angle for finiteness of its expectation when player I maximizes the distance to the boundary and player II minimizes the distance. There is also a critical angle such that for smaller angles, player II can...

This paper provides a novel proof for the sufficiency of certain well-known criteria that guarantee the martingale property of a continuous, nonnegative local martingale. More precisely, it is shown that generalizations of Novikov’s condition and Kazamaki’s criterion follow directly from the...

We study approximations of reflected Itô diffusions on convex subsets D of Rd by solutions of stochastic differential equations with penalization terms. We assume that the diffusion coefficients are merely measurable functions. In the case of Lipschitz continuous coefficients we give the rate...