The first passage problem for generalized Ornstein-Uhlenbeck processes with non-positive jumps

Dimitar I. Hadjiev

Séminaire de probabilités de Strasbourg (1985)

  • Volume: 19, page 80-90

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Hadjiev, Dimitar I.. "The first passage problem for generalized Ornstein-Uhlenbeck processes with non-positive jumps." Séminaire de probabilités de Strasbourg 19 (1985): 80-90. <http://eudml.org/doc/113539>.

@article{Hadjiev1985,
author = {Hadjiev, Dimitar I.},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {martingale techniques; Laplace transform; first passage time; time-change},
language = {eng},
pages = {80-90},
publisher = {Springer - Lecture Notes in Mathematics},
title = {The first passage problem for generalized Ornstein-Uhlenbeck processes with non-positive jumps},
url = {http://eudml.org/doc/113539},
volume = {19},
year = {1985},
}

TY - JOUR
AU - Hadjiev, Dimitar I.
TI - The first passage problem for generalized Ornstein-Uhlenbeck processes with non-positive jumps
JO - Séminaire de probabilités de Strasbourg
PY - 1985
PB - Springer - Lecture Notes in Mathematics
VL - 19
SP - 80
EP - 90
LA - eng
KW - martingale techniques; Laplace transform; first passage time; time-change
UR - http://eudml.org/doc/113539
ER -

References

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  1. 1. J.-M. Bismut, Calcul des variations et processus de sauts, Z. Wahr. verw. Geb.63 (1983), No.2, pp.147-236. Zbl0494.60082MR701527
  2. 2. D.A. Darling and A.J.F. Siegert, The first passage problem for a continuous Markov process, Ann. Math. Statist.24 (1953), pp.624-639. Zbl0053.27301MR58908
  3. 3. J. Jacod, Calcul stochastique et problèmes de martingales, Lecture Notes in Math. vol.714, Springer-Verlag, 1979. Zbl0414.60053MR542115
  4. 4. E. Lukacs, Stochastic convergence, Acad.Press, 1975. Zbl0312.60011MR375405
  5. 5. V. Mackevicius, On some problems of optimal stopping of stable stochastic processes, Lietuvos Mat. Rink. 12 (1972), No.1, pp.173-180 (in Russian). MR347016
  6. 6. A.A. Novikov, Martingale approach to the firs passage time problems for nonlinear boundaries, Proc. Steklov Math. Inst.158 (1981), pp.130-152 (in Russian). Zbl0491.60038MR662841
  7. 7. L.A. Shepp, Explicit solutions to some problems of optimal stopping, Ann. Math. Statist.40 (1969), No.3, pp.993-1010. Zbl0177.22301MR250415
  8. 8. A.V. Skorokhod, Random processes with independent increments, Nauka, 1964 (in Russian). MR860563
  9. 9. H.M. Taylor, Optimal stopping in a Markov process, Ann. Math. Statist.39 (1968), pp.1333-1344. Zbl0177.45702MR232444

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