Related papers: Brownian Bridges on Random Intervals
We provide a general model for Brownian motions on metric graphs with interactions. In a general setting, for (sticky) Brownian propagations on edges, our model provides a characterization of lifetimes and holding times on vertices in terms…
We give a probabilistic representation of a one-dimensional diffusion equation where the solution is discontinuous at $0$ with a jump proportional to its flux. This kind of interface condition is usually seen as a semi-permeable barrier.…
In recent times we hear increasingly often about cyber attacks on various commercial and strategic sites that manage to escape any defense. In this article, we model such attacks on networks via stochastic processes and predict the time of…
We construct a stochastic process whose drift is a function of the process's local time at a reflecting barrier. The process arose as a model of the interactions of a Brownian particle and an inert particle in (Knight, 2001). Interesting…
Throughout physics Brownian dynamics are used to describe the behaviour of molecular systems. When the Brownian particle is confined to a bounded domain, a particularly important question arises around determining how long it takes the…
In this paper we investigate the behavior of the bridges of a Markov counting process in several directions. We first characterize convexity(concavity) in time of the mean value in terms of lower (upper) bounds on the so called…
We study the rate of convergence of two discrete processes towards the Brownian bridge: the random walk conditioned to be zero at time 2n and the empirical process which appears in the Glivencko-Cantelli theorem. Combining a functional…
We consider a market model where there are two levels of information. The public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can…
We consider a gas of independent Brownian particles on a bounded interval in contact with two particle reservoirs at the endpoints. Due to the Brownian nature of the particles, infinitely many particles enter and leave the system in each…
Prediction of events in financial markets is every investor's dream and, usually, wishful thinking. From a more general, economic and societal viewpoint, the identification of indicators for large events is highly desirable to assess…
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.…
One problem of wide interest involves estimating expected crossing-times. Several tools have been developed to solve this problem beginning with the works of Wald and the theory of sequential analysis. An extension of his approach is…
We consider the problem of leakage or effusion of an ensemble of independent stochastic processes from a region where they are initially randomly distributed. The case of Brownian motion, initially confined to the left half line with…
We revisit classical asymptotics when testing for a structural break in linear regression models by obtaining the limit theory of residual-based and Wald-type processes. First, we establish the Brownian bridge limiting distribution of these…
We consider non-colliding Brownian bridges starting from two points and returning to the same position. These positions are chosen such that, in the limit of large number of bridges, the two families of bridges just touch each other forming…
Many inverse problems require reconstructing physical fields from limited and noisy data while incorporating known governing equations. A growing body of work within probabilistic numerics formalizes such tasks via Bayesian inference in…
In applications spaning from image analysis and speech recognition, to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a…
Aldous and Pitman (1994) studied asymptotic distributions, as n tends to infinity, of various functionals of a uniform random mapping of a set of n elements, by constructing a mapping-walk and showing these mapping-walks converge weakly to…
We suggest a model for data losses in a single node of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. The model shows critical behavior with an abrupt…
The laws of chance are often subtle and deceptive. This is why games of chance work. People are convinced that they obey seemingly intuitive laws, while the underlying mathematical structure reveals a different and more complex reality.…