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Yuval Peres
Yuval Peres
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This conditioning of a Bessel process is Dooba Doob transform. For $\rho$ in $(0,2)$ it leads to a Bessel process of dimension $4-\rho$. See Goeing-Jaeschke, A., Yor, M. (2003) A Survey on some generalizations of Bessel processes. Bernoulli 9, 313–349 and the book by Revuz-Yor, Continuous Martingales and BM. the LIL for Bessel processes is the same as for Brownian motion and is thus not affected by the conditioning. See (Revuz and Yor, 1994, Exercise X1.1.20).

This conditioning of a Bessel process is Doob transform. For $\rho$ in $(0,2)$ it leads to a Bessel process of dimension $4-\rho$. See Goeing-Jaeschke, A., Yor, M. (2003) A Survey on some generalizations of Bessel processes. Bernoulli 9, 313–349.

This conditioning of a Bessel process is a Doob transform. For $\rho$ in $(0,2)$ it leads to a Bessel process of dimension $4-\rho$. See Goeing-Jaeschke, A., Yor, M. (2003) A Survey on some generalizations of Bessel processes. Bernoulli 9, 313–349 and the book by Revuz-Yor, Continuous Martingales and BM. the LIL for Bessel processes is the same as for Brownian motion and is thus not affected by the conditioning. See (Revuz and Yor, 1994, Exercise X1.1.20).

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Yuval Peres
Yuval Peres
  • 14.2k
  • 1
  • 28
  • 49

This conditioning of a Bessel process is Doob transform. For $\rho$ in $(0,2)$ it leads to a Bessel process of dimension $4-\rho$. See Goeing-Jaeschke, A., Yor, M. (2003) A Survey on some generalizations of Bessel processes. Bernoulli 9, 313–349.