We consider N independent stochastic processes (Xi(t), t ∈ [0, Ti]), i = 1, . . . , N , defined by a stochastic differential equation with drift term depending on a random variable φi. The distribution of the random effect φi depends on unknown parameters which are to be estimated from the continuous observation of the processes Xi. We give the expression of the exact likelihood. When the drift...

We study a continuous-time random walk on the d-dimensional lattice, subject to a drift and an attraction to large clusters of a subcritical Bernoulli site percolation. We find two distinct regimes: a ballistic one, and a subballistic one taking place when the attraction is strong enough. We identify the speed in the former case, and the algebraic rate of escape in the latter case. Finally, we ...

Joël De Coninck, François Dunlop, Thierry Huillet Abstract: We consider random walks Xn in Z+, obeying a detailed balance condition, with a weak drift towards the origin when Xn ր ∞. We reconsider the equivalence in law between a random walk bridge and a 1+1 dimensional Solid-On-Solid bridge with a corresponding Hamiltonian. Phase diagrams are discussed in terms of recurrence versus wetting. A ...

In this paper sequential monitoring schemes to detect nonparametric drifts are studied for the random walk case. The procedure is based on a kernel smoother. As a by-product we obtain the asymptotics of the Nadaraya-Watson estimator and its associated sequential partial sum process under non-standard sampling. The asymptotic behavior differs substantially from the stationary situation, if there...

When a distinct cultural region forms, its rate of absorption into the surrounding culture may be an important variable to take into account when attempting to minimise conflict. This paper describes a re-implementation of Axelrod’s agentbased model of cultural dissemination, and uses it to investigate how random drift influences the longevity of distinct regions. Cultural regions are found to ...

We consider the problem of data-stream classification, introducing a stream-classification algorithm, Dynamic Streaming Random Forests, that is able to handle evolving data streams using an entropy-based drift-detection technique. The algorithm automatically adjusts its parameters based on the data seen so far. Experimental results show that the algorithm handles multi-class problems for which ...

A simple asymmetric random walk on the integers is stopped when its range is of a given length. When and where is it stopped? Analogous questions can be stated for a Brownian motion. Such problems are studied using results for the classical ruin problem, yielding results for the cover time and the range, both for asymmetric random walks and Brownian motion with drift.

We consider families of random dynamical systems induced by parametrized one dimensional stochastic diierential equations. We give necessary and suucient conditions on the invariant measures of the associated Markov semigroups which ensure a stochastic bifurcation. This leads to suucient conditions on drift and diiusion coeecients for a stochastic pitchfork and transcritical bifurcation of the ...

We prove the annealed Central Limit Theorem for random walks in bistochastic random environments on Zd with zero local drift. The proof is based on a “dynamicist’s interpretation” of the system, and requires a much weaker condition than the customary uniform ellipticity. Moreover, recurrence is derived for d ≤ 2. Mathematics Subject Classification: 60G50, 60K37, 37A50 (60F05, 60G42, 37A20, 37H9...

In this paper we study the problem of tracking a random walk observed with noise when the variance of the walk increment is unknown. We describe a sequence of estimators of the random walk and we design an algorithm to choose the best estimator among all the sequence. We give also a bound for the mean square error of this estimator. Finally some simulations are presented and we compare our algo...