Related papers: Monotonicity and robustness in Wiener disorder det…
The multiple disorder problem seeks to determine a sequence of stopping times which are as close as possible to the unknown times of disorders at which the observation process changes its probability characteristics. We derive closed form…
We construct a Bayesian sequential test of two simple hypotheses about the value of the unobservable drift coefficient of a Brownian motion, with a possibility to change the initial decision at subsequent moments of time for some penalty.…
We consider a stochastic differential equation involving standard and fractional Brownian motion with unknown drift parameter to be estimated. We investigate the standard maximum likelihood estimate of the drift parameter, two non-standard…
In the classical quickest detection problem, one must detect as quickly as possible when a Brownian motion without drift "changes" into a Brownian motion with positive drift. The change occurs at an unknown "disorder" time with exponential…
We consider the problem of estimating the roughness of the volatility process in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion with drift. To this end, we introduce a new estimator that…
In sequential change detection, existing performance measures differ significantly in the way they treat the time of change. By modeling this quantity as a random time, we introduce a general framework capable of capturing and better…
The input-output behaviour of the Wiener neuronal model subject to alternating input is studied under the assumption that the effect of such an input is to make the drift itself of an alternating type. Firing densities and related…
Consider the motion of a Brownian particle in two or more dimensions, whose coordinate processes are standard Brownian motions with zero drift initially, and then at some random/unobservable time, one of the coordinate processes gets a…
We study a classical Bayesian statistics problem of sequentially testing the sign of the drift of an arithmetic Brownian motion with the $0$-$1$ loss function and a constant cost of observation per unit of time for general prior…
We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long range behavior of the…
We establish a monotonicity property in the space variable for the solutions of an initial boundary value problem concerned with the parabolic partial differential equation connected with super-Brownian motion.
In this paper we investigate a problem of large deviations for continuous Volterra processes under the influence of model disturbances. More precisely, we study the behavior, in the near future after $T$, of a Volterra process driven by a…
We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…
The operation of Brownian motors is usually described in terms of out-of-equilibrium and symmetry-breaking settings, with the relevant spatiotemporal symmetries identified from the analysis of the equations of motion for the system at hand.…
In two preceding articles, we studied the problem of the existence and uniqueness of a solution to some general BSDE on manifolds. In these two articles, we assumed some Lipschitz conditions on the drift $f(b,x,z)$. The purpose of this…
We obtain exact asymptotic results for the disorder averaged persistence of a Brownian particle moving in a biased Sinai landscape. We employ a new method that maps the problem of computing the persistence to the problem of finding the…
We study reflecting Brownian motion with drift constrained to a wedge in the plane. Our first set of results provide necessary and sufficient conditions for existence and uniqueness of a solution to the corresponding submartingale problem…
The invariance properties of Brownian motion are investigated and revisited within a recent Lie symmetry approach to stochastic differential equations. Some notable properties of the process can be recovered by a related integration by…
We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…
We consider the extent to which we can learn from a completely randomized experiment whether all individuals have treatment effects that are weakly of the same sign, a condition we call monotonicity. From a classical sampling perspective,…