Back
 JAMP  Vol.4 No.7 , July 2016
Skorohod Integral at Vacuum State on Guichardet-Fock Spaces
Abstract:

In this paper, we define expectation of fF, i.e. E(f)=f(?), according to Wiener-Ito-Segal isomorphic relation between Guichardet-Fock space F and Wienerspace W. Meanwhile, we derive a formula for the expectation of random Hermite polynomial in Skorohod integral on Guichardet- Fock spaces. In particular, we prove that the anticipative Girsanov identities under the condition E(Hx(δ(x),x2)),n1 on Guichardet-Fock spaces.

Cite this paper: Zhang, J. , Li, Y. and Sun, X. (2016) Skorohod Integral at Vacuum State on Guichardet-Fock Spaces. Journal of Applied Mathematics and Physics, 4, 1321-1326. doi: 10.4236/jamp.2016.47141.
References

[1]   Hudson, R.L. and Parthasarathy, K.R. (1984) Quantum Ito’s Formula and Stochastic Evolutions. Communications in Mathematical Physics, 3, 301-323. http://dx.doi.org/10.1007/BF01258530

[2]   Wang, C.S., Lu, Y.C. and Chai, H.F. (2011) An Alternative Approach to Privault’s Discrete-Time Chaotic Calculus. Journal of Mathematical Analysis and Applications, 2, 643-654. http://dx.doi.org/10.1016/j.jmaa.2010.08.021

[3]   Zhang, J.H., Wang, C.S. and Tian, L.N. (2015) Localization of Unbounded Operators on Guichardet Spaces. Journal of Applied Mathematics and Physics, 3, 792-796. http://dx.doi.org/10.4236/jamp.2015.37096

[4]   Attal, S. and Lindsay, J.M. (2004) Quantum Stochastic Calculus with Maximal Operator Domains. The Annals of Probability, 32, 488-529. http://dx.doi.org/10.1214/aop/1078415843

[5]   Privault, N. (2009) Moment Identities for Skorohod Integrals on the Wiener Space and Applications. Electronic Communications in Probability, 14, 116-121. http://dx.doi.org/10.1214/ECP.v14-1450

[6]   Privault, N. (2010) Random Hermite Polynomials and Girsanov Identities on the Wiener Space. Infinite Dimensional Analysis, 13, 663-675.

 
 
Top