On distributions of integral functionals of diffusions stopped at inverse range time
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 24, Tome 454 (2016), pp. 43-51
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In the paper we develop the methods for computations of distributions of integral functionals of diffusions stopped at inverse range time. We consider also the moment, which is the minimum of inverse range time and the exponentially distributed stopping time independent of the diffusion. An interesting example of the applications of these methods is considered.
[1] J. P. Imhof, “On the range of Brownian motion and its inverse process”, Ann. Probab., 13 (1985), 1–13 | DOI | MR
[2] P. Vallois, “Decomposition of the Brownian path via the range process”, Stoch. Proc. Appl., 55 (1995), 211–226 | DOI | MR | Zbl
[3] A. N. Borodin, “O raspredelenii funktsionalov ot brounovskogo dvizheniya, ostanovlennogo v moment, obratnyi k razmakhu”, Zap. nauchn. semin. POMI, 260, 1999, 50–72 | MR | Zbl
[4] A. N. Borodin, Sluchainye protsessy, Lan, Sankt-Peterburg, 2013
[5] A. N. Borodin, P. Salminen, Spravochnik po brounovskomu dvizheniyu. Fakty i formuly, Lan, Sankt-Peterburg, 2016