Skorokhod Embedding by Randomized Hitting Times

Fitzsimmons, P. J.

doi:10.1007/978-1-4684-0562-0_8

Cited by 5 publications

(2 citation statements)

References 6 publications

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“…In [38] (with some minor correction recorded in [39]) an existence theorem for embedding in a general Markov process is obtained as a by-product of investigation of a natural extention of Hunt's balayage L B m (see [38] for appropriate definitions). The second paper [40], is devoted to the Skorokhod problem for general right Markov processes. Suppose that X 0 ∼ ν and the potentials of ν and µ are σ-finite and µU X ≤ νU X .…”

Section: Rost (1971)mentioning

confidence: 99%

The Skorokhod embedding problem and its offspring

Obłój¹

2004

Probab. Surveys

237

120

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This is a survey about the Skorokhod embedding problem. It presents all known solutions together with their properties and some applications. Some of the solutions are just described, while others are studied in detail and their proofs are presented. A certain unification of proofs, based on one-dimensional potential theory, is made. Some new facts which appeared in a natural way when different solutions were cross-examined, are reported. Az\'ema and Yor's and Root's solutions are studied extensively. A possible use of the latter is suggested together with a conjecture.Comment: Published at http://dx.doi.org/10.1214/154957804100000060 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Section: Rost (1971)mentioning

confidence: 99%

The Skorokhod embedding problem and its offspring

Obłój¹

2004

Probab. Surveys

237

120

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show abstract

“…REMARK 1.4. Let us note that Corollary 1.3 has the following consequence related to Skorokhod stopping (see [11,4,6,5,1]). Let ν be a probability measure on X and let (X(t)) be Brownian motion or an α-stable process on X with initial distribution ν.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Convexity properties of harmonic measures

Hansen

Netuka

2008

Advances in Mathematics

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It is shown that, given a point x ∈ Ê d , d ≥ 2, and open sets U 1 , . . . , U k in Ê d containing x, any convex combination of the harmonic measures ε U c n x for x with respect to U n , 1 ≤ n ≤ k, is the limit of a sequence (εThis answers a question raised in connection with Jensen measures.More generally, we prove that, for arbitrary measures on an open set W , the set of extremal representing measures, with respect to the cone of continuous potentials on W or with respect to the cone of continuous functions on W which are superharmonic W , is dense in the compact convex set of all representing measures. This is achieved approximating balayage on open sets by balayage on unions of balls which are pairwise disjoint and very small with respect to their mutual distances and then shrinking these balls in a suitable manner.The results are presented simultaneously for the classical case and for the theory of Riesz potentials.Finally, a characterization of all Jensen measures and of all extremal Jensen measures is given.

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Smooth measures and continuous additive functionals of right Markov processes

Fitzsimmons

Getoor

1996

Itô’s Stochastic Calculus and Probability Theory

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Skorokhod Embedding by Randomized Hitting Times

Cited by 5 publications

References 6 publications

The Skorokhod embedding problem and its offspring

The Skorokhod embedding problem and its offspring

Convexity properties of harmonic measures

Smooth measures and continuous additive functionals of right Markov processes

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