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Averaging problems of running processes associated with Brownian motion and applications

Bao Quoc Ta

Department of Mathematics and Statistics, Åbo Akademi University, FIN-20500 Åbo, Finland

Department of Applied Mathematics, Faculty of Information Technology, National University of Civil Engineering, 55 Giai Phong Road, Hanoi, Vietnam

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https://doi.org/10.1142/S0129167X15500287Cited by:0 (Source: Crossref)

Abstract

Recently the new technique to solve optimal stopping problems for Hunt processes is developed (see [S. Christensen, P. Salminen and B. Q. Ta, Optimal stopping of strong Markov processes, Stochastic Process. Appl. 123(3) (2013) 1138–1159]). The crucial feature of the approach is to utilize the representation of the r-excessive functions as expected suprema. However, it seems to be difficult when applying directly the approach to some concrete cases, e.g. one-sided problem for reflecting Brownian motion and two-sided problem for Brownian motion. In this paper, we review and exploit this approach to find explicit solutions of two problems above.

Keywords:

AMSC: 60G40, 60J65, 60J25

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