We consider the Itô SDE with a non-degenerate diffusion coefficient and a measurable drift coefficient. Under the condition that the gradient of the diffusion coefficient and the divergences of the diffusion and drift coefficients are exponentially integrable with respect to the Gaussian...

Here, we study the asymptotic behavior of the maximum local time of the diffusion in Brownian environment. Shi (1998) [17] proved that, surprisingly, the maximum speed of is at least tlog(log(logt)); whereas in the discrete case, it is t. We show that tlog(log(logt)) is the proper rate and...

We provide a rate for the strong convergence of Euler approximations for stochastic differential equations (SDEs) whose diffusion coefficient is not Lipschitz but only (1/2+[alpha])-Hölder continuous for some [alpha]>=0.

The Hybrid Monte Carlo (HMC) algorithm provides a framework for sampling from complex, high-dimensional target distributions. In contrast with standard Markov chain Monte Carlo (MCMC) algorithms, it generates nonlocal, nonsymmetric moves in the state space, alleviating random walk type behaviour...

We establish large deviation properties valid for almost every sample path of a class of stationary mixing processes (X1,...,Xn,...). These properties are inherited from those of and describe how the local fluctuations of almost every realization of Sn deviate from the almost sure behavior....

We explore properties of the value function and existence of optimal stopping times for functionals with discontinuities related to the boundary of an open (possibly unbounded) set . The stopping horizon is either random, equal to the first exit from the set , or fixed (finite or infinite). The...

Conditions for the existence of strictly stationary multivariate GARCH processes in the so-called BEKK parametrisation, which is the most general form of multivariate GARCH processes typically used in applications, and for their geometric ergodicity are obtained. The conditions are that the...

By constructing a new coupling, the log-Harnack inequality is established for the functional solution of a delay stochastic differential equation with multiplicative noise. As applications, the strong Feller property and heat kernel estimates w.r.t. quasi-invariant probability measures are...

We analyze a sequence of single-server queueing systems with impatient customers in heavy traffic. Our state process is the offered waiting time, and the customer arrival process has a state dependent intensity. Service times and customer patient-times are independent; i.i.d. with general...