Infinite-dimensional elliptic operators and parabolic equations connected with them

Daletskii, Yu. L.

doi:10.1070/rm1967v022n04abeh003769

Cited by 79 publications

(35 citation statements)

References 2 publications

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“…Stochastic integration with respect to cylindrical Brownian processes is developed for example in Daletskij [4], followed by the articles Gaveau [6], Lepingle and Ouvrard [14] and many others. Surprisingly, stochastic integration with respect to other cylindrical processes than cylindrical Brownian motion is much less considered.…”

Section: Introductionmentioning

confidence: 99%

Stochastic integration with respect to cylindrical Lévy processes

Jakubowski¹,

Riedle²

2017

Ann. Probab.

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A cylindrical Lévy process does not enjoy a cylindrical version of the semimartingale decomposition which results in the need to develop a completely novel approach to stochastic integration. In this work, we introduce a stochastic integral for random integrands with respect to cylindrical Lévy processes in Hilbert spaces. The space of admissible integrands consists of adapted stochastic processes with values in the space of Hilbert-Schmidt operators. Neither the integrands nor the integrator is required to satisfy any moment or boundedness condition. The integral process is characterised as an adapted, Hilbert space valued semi-martingale with càdlàg trajectories.

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Section: Introductionmentioning

confidence: 99%

Stochastic integration with respect to cylindrical Lévy processes

Jakubowski¹,

Riedle²

2017

Ann. Probab.

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“…Here Φ i {s 9 ω) 9 i = 1,2 is ffor if-process> respectively, with suitable additional conditions. Similar problem concerning Hubert space valued Brownian motion has been discussed by Daletskii [1], 1. Preliminaries.…”

Section: A Mapping X T (ω); [0and>)xω-±h Is Called An H-valued Stochasmentioning

confidence: 83%

Stochastic Integrals Based on Martingales Taking Values in Hilbert Space

Kunita

1970

Nagoya Mathematical Journal

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“…We are therefore able to construct a Hubert scale derived from ώ (for definition see Yu. L. Daletskii [7] We are now ready to state our main results. The equation (1) has a unique solution on i2*_ 1/2J which comes from the discussion in § 2.…”

Section: ) DX T = -ώX T Dt + Db T On H = D ([0 Tγ]) Where B T Is Amentioning

confidence: 99%

Infinite dimensional Langevin equation and Fokker-Planck equation

Miyahara

1981

Nagoya Mathematical Journal

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Stochastic processes on a Hilbert space have been discussed in connection with quantum field theory, theory of partial differential equations involving random terms, filtering theory in electrical engineering and so forth, and the theory of those processes has greatly developed recently by many authors (A. B. Balakrishnan [1, 2], Yu. L. Daletskii [7], D. A. Dawson [8, 9], Z. Haba [12], R. Marcus [18], M. Yor [26]).

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Infinite-dimensional elliptic operators and parabolic equations connected with them

Cited by 79 publications

References 2 publications

Stochastic integration with respect to cylindrical Lévy processes

Stochastic integration with respect to cylindrical Lévy processes

Stochastic Integrals Based on Martingales Taking Values in Hilbert Space

Infinite dimensional Langevin equation and Fokker-Planck equation

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