White noise approach to stochastic integration. (English) Zbl 1119.60038
By introducing the notion of white noise adaptedness and proving the white noise analogue of the scalar type integrator inequalities introduced by L. Accardi, F. Fagnola and J. Quaegebeur [J. Funct. Anal. 104, No. 1, 149–197 (1992; Zbl 0759.60068)] which, in their terms, generalize the Hudson-Parthasarathy basic estimates of stochastic integrals, the authors show that some Hida distributions are in fact elements of the Fock space. The obtained inequalities are used to prove an analogue regularity result for solutions of white noise equations with bounded coefficients.
Reviewer: Mikhail P. Moklyachuk (Kyïv)
Citations:
Zbl 0759.60068References:
| [1] | DOI: 10.1016/0022-1236(92)90094-Y · Zbl 0759.60068 · doi:10.1016/0022-1236(92)90094-Y |
| [2] | L. Accardi, F. Fagnola. Stochastic Integration, in Quantum Probability and Aplication III, Lecture Notes in Math., 1303, 6-19, Springer-Verlag, New York (1988). |
| [3] | L. Accardi, I. V. Vlovich and Y. G. Lu. A White Noise Approach to Classical and Quantum Stochastic Calculus, Volterra Preprint 375, Rome, July (1999). |
| [4] | L.Accardi. Quantum Probability: An Introduction to Some Basic Ideas and Trends, Modelos Estocasticos II 16, Sociedad Mathematica Mexicana (2001). · Zbl 1033.81048 |
| [5] | DOI: 10.1016/0022-1236(89)90036-0 · Zbl 0669.60099 · doi:10.1016/0022-1236(89)90036-0 |
| [6] | L. Accardi, Y. G. Lu, I. V. Volovich. Quantum theory and its stochastic limit. Springer Verlag (2002). · Zbl 1140.81307 |
| [7] | Accardi L., Lu Y.G., Volovich I. Nonlinear extensions of classical and quantum stochastic calculus and essentially infinite dimensional analysis, in: Probability Towards 2000; L. Accardi, Chris Heyde (eds.) Springer LN in Statistics 128, 1- 33, (1998). Proceedings of the Symposium: Probability towards two thousand, Columbia University, New York, 2-6, October, (1995). · Zbl 1044.81647 |
| [8] | S. Attal and J. M. Lindsay. Quantum Stochastic Calculus with maximal operator domains. The annales of probability. Vol 32 (2004). · Zbl 1053.81053 |
| [9] | P. Biane. Calcul Stochastique non-commutatif, Seminaire de Probabilites XXIX. Lecture Note in Math. Springer, Berlin (1608). |
| [10] | T. Hida. Brownian Motion. Springer (1992). · Zbl 0327.60049 |
| [11] | DOI: 10.1007/BF01258530 · Zbl 0546.60058 · doi:10.1007/BF01258530 |
| [12] | H. Kuo. White Noise Distribution Theory. C.R.C Press, Boca Raton, New York, London, Tokyo (1996). · Zbl 0853.60001 |
| [13] | K. R. Parthasarathy. An Introduction to Quantum Stochastic Calculus. Birkhauser Verlag, Basel, Boston, Berlin (1992). · Zbl 0751.60046 |
| [14] | P. A. Meyer. Quantum Probability for Probabilists. Springer, Berlin (1993). · Zbl 0773.60098 |
| [15] | K. Yosida. Functional Analysis. Springer (1978). |
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