The Experts below are selected from a list of 99 Experts worldwide ranked by ideXlab platform
Jasmin A L Roder - One of the best experts on this subject based on the ideXlab platform.
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path dependent backward stochastic volterra integral equations with jumps differentiability and duality principle
Probability Uncertainty and Quantitative Risk, 2018Co-Authors: Ludger Overbeck, Jasmin A L RoderAbstract:We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations (BSVIEs) with jumps, where path-dependence means the dependence of the free term and generator of a path of a Cadlag Process. Furthermore, we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation (FSVIE) with jumps and a linear path-dependent BSVIE with jumps. As a result of the duality principle we get a comparison theorem and derive a class of dynamic coherent risk measures based on path-dependent BSVIEs with jumps.
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Path-Dependent Backward Stochastic Volterra Integral Equations with Jumps
SSRN Electronic Journal, 2016Co-Authors: Ludger Overbeck, Jasmin A L RoderAbstract:We study existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations (BSVIEs) with jumps. Path-dependence means the dependence of both the free term and the generator of a path of a Cadlag Process. Furthermore, we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation (FSVIE) with jumps and a linear path-dependent BSVIE with jumps.
Xue Peng - One of the best experts on this subject based on the ideXlab platform.
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Positivity Preserving Semigroups and Positivity Preserving Coercive Forms
Stochastic Partial Differential Equations and Related Fields, 2018Co-Authors: Xian Chen, Xue PengAbstract:We recall the idea of Ma and Rockner (Canad. J. Math., 47:817–840, 1995, [13]) and report some further progress along the line of the research initiated by Ma and Rockner (Canad. J. Math., 47:817–840, 1995, [13]). The further progress includes the technique of \(h\hat{h}\)-transformations for positivity preserving semigroups, and includes our recent results on (\(\sigma \)-finite) distribution flows associated with a given positivity preserving coercive form, which is independent of the choice of h, and equipped with which the canonical Cadlag Process behaves like a strong Markov Process.
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Distribution flows associated with positivity preserving coercive forms
arXiv: Probability, 2017Co-Authors: Xian Chen, Xue PengAbstract:For a given quasi-regular positivity preserving coercive form, we construct a family of ($\sigma$-finite) distribution flows associated with the semigroup of the form. The canonical Cadlag Process equipped with the distribution flows behaves like a strong Markov Process. Moreover, employing distribution flows we can construct optional measures and establish Revuz correspondence between additive functionals and smooth measures. The results obtained in this paper will enable us to perform a kind of stochastic analysis related to positivity preserving coercive forms.
Raouf Ghomrasni - One of the best experts on this subject based on the ideXlab platform.
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Integral and local limit theorems for level crossings of diffusions and the Skorohod problem
Electronic Journal of Probability, 2014Co-Authors: Rafał M. Łochowski, Raouf GhomrasniAbstract:Using a new technique, based on the regularisation of a Cadlag Process via the double Skorohod map, we obtain limit theorems for integrated numbers of level crossings of diffusions. This result is related to the recent results on the limit theorems for the truncated variation. We also extend to diffusions the classical result of Kasahara on the "local" limit theorem for the number of crossings of a Wiener Process. We establish the correspondence between the truncated variation and the double Skorohod map. Additionally, we prove some auxiliary formulas for the Skorohod map with time-dependent boundaries.
Ludger Overbeck - One of the best experts on this subject based on the ideXlab platform.
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path dependent backward stochastic volterra integral equations with jumps differentiability and duality principle
Probability Uncertainty and Quantitative Risk, 2018Co-Authors: Ludger Overbeck, Jasmin A L RoderAbstract:We study the existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations (BSVIEs) with jumps, where path-dependence means the dependence of the free term and generator of a path of a Cadlag Process. Furthermore, we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation (FSVIE) with jumps and a linear path-dependent BSVIE with jumps. As a result of the duality principle we get a comparison theorem and derive a class of dynamic coherent risk measures based on path-dependent BSVIEs with jumps.
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Path-Dependent Backward Stochastic Volterra Integral Equations with Jumps
SSRN Electronic Journal, 2016Co-Authors: Ludger Overbeck, Jasmin A L RoderAbstract:We study existence and uniqueness of a solution to path-dependent backward stochastic Volterra integral equations (BSVIEs) with jumps. Path-dependence means the dependence of both the free term and the generator of a path of a Cadlag Process. Furthermore, we prove path-differentiability of such a solution and establish the duality principle between a linear path-dependent forward stochastic Volterra integral equation (FSVIE) with jumps and a linear path-dependent BSVIE with jumps.
Jan Rosiński - One of the best experts on this subject based on the ideXlab platform.
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On the uniform convergence of random series in Skorohod space and representations of càdlàg infinitely divisible Processes
The Annals of Probability, 2013Co-Authors: Andreas Basse-o'connor, Jan RosińskiAbstract:Let Xn be independent random elements in the Skorohod space D([0,1];E) of Cadlag functions taking values in a separable Banach space E. Let Sn=∑nj=1Xj. We show that if Sn converges in finite dimensional distributions to a Cadlag Process, then Sn+yn converges a.s. pathwise uniformly over [0,1], for some yn∈D([0,1];E). This result extends the Ito–Nisio theorem to the space D([0,1];E), which is surprisingly lacking in the literature even for E=R. The main difficulties of dealing with D([0,1];E) in this context are its nonseparability under the uniform norm and the discontinuity of addition under Skorohod’s J1-topology. We use this result to prove the uniform convergence of various series representations of Cadlag infinitely divisible Processes. As a consequence, we obtain explicit representations of the jump Process, and of related path functionals, in a general non-Markovian setting. Finally, we illustrate our results on an example of stable Processes. To this aim we obtain new criteria for such Processes to have Cadlag modifications, which may also be of independent interest.
