Ilie Grigorescu

Assoc. Professor

Phone:
(305) 284-2146
Locator Code:
4250
 
Career

Education

1997Ph.D. New York University

LIST OF SPECIALTIES: Probability, PDE

Research

LIST OF SPECIALTIES: Probability, PDE

Publications

I Grigorescu, M Kang "Hydrodynamic limit for a Fleming–Viot type system" Stochastic processes and their applications 111-143110, 1 (North-Holland. 2004/3/1).

SUMMARY:
We consider a system of N Brownian particles evolving independently in a domain D. As soon as one particle reaches the boundary it is killed and one of the other particles is chosen uniformly and splits into two independent particles resuming a new cycle of independent motion until the next boundary hit. We prove the hydrodynamic limit for the joint law of the empirical measure process and the average number of visits to the boundary as N approaches infinity.

Ilie Grigorescu, Min Kang "Brownian motion on the figure eight" Journal of Theoretical Probability 817-84415, 3 (Kluwer Academic Publishers-Plenum Publishers. 2002/7/1). [Link]

SUMMARY:
In an interval containing the origin we study a Brownian motion which returns to zero as soon as it reaches the boundary. We determine explicitly its transition probability, prove it is ergodic and calculate the decay rate to equilibrium. It is shown that the process solves the martingale problem for certain asymmetric boundary conditions and can be regarded as a diffusion on an eight shaped domain. In the case the origin is situated at a rationally commensurable distance from the two endpoints of the interval we give the complete characterization of the possibility of collapse of distinct paths.

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