In this work we study rough differential equations driven by a fractional Brownian motion with Hurst parameter H>14 and establish Varadhan’s small time estimates for the density of solutions of such equations under Hörmander’s type conditions.

We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded single-type process composed of all individuals having the same...

In this article, it is proved that for any probability law μ over R and a drift field b:R→R and killing field k:R→R+ which satisfy hypotheses stated in the article and a given terminal time t0, there exists a string m, an α∈(0,1], an initial condition x0∈R and a process X with...

Asymptotic expansions are derived as power series in a small coefficient entering a nonlinear multiplicative noise and a deterministic driving term in a nonlinear evolution equation. Detailed estimates on remainders are provided.

Based on the theory of M-matrix and Perron–Frobenius theorem, we provide some criteria to justify the convergence of the regime-switching diffusion processes in Wasserstein distances. The cost function we used to define the Wasserstein distance is not necessarily bounded. The continuous time...

We obtain error terms on the rate of convergence to Extreme Value Laws, and to the asymptotic Hitting Time Statistics, for a general class of weakly dependent stochastic processes. The dependence of the error terms on the ‘time’ and ‘length’ scales is very explicit. Specialising to data...

We prove the existence of the integrated density of states for subordinate Brownian motions in the presence of the Poissonian random potentials on the Sierpiński gasket.

We provide an equivalent log-concavity condition to the mean residual life (MRL) ordering for real-valued processes. This result, combined with classical properties of total positivity of order 2, allows to exhibit new families of integrable processes which increase in the MRL order (MRL...

The convergence of properly time-scaled and normalized maxima of independent standard Brownian motions to the Brown–Resnick process is well-known in the literature. In this paper, we study the extremal functional behavior of non-Gaussian processes, namely squared Bessel processes and scalar...

We investigate the asymptotic behavior of the least squares estimator of the unknown parameters of random coefficient bifurcating autoregressive processes. Under suitable assumptions on inherited and environmental effects, we establish the almost sure convergence of our estimates. In addition,...