Stochastic evolutions driven by non-linear white noise

• Autorzy: Accardi, L. , Boukas, A.
• Języki publikacji: EN

Abstrakty

EN

We prove the existence and uniqueness theorem for stochastic differential equations with bounded coefficients driven by the renormalized square of white noise.These equations are interpreted as sesquilinear forms on the linear span of the exponential vectors (of the first order white noise) and the existence theorem is establishedon the space of these forms.

Słowa kluczowe

EN

stochastic differential equations; square of white noise; exponential vectors

• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2002
• Tom: Vol. 22, Fasc. 1
• Strony: 141--154
• Opis fizyczny: Biblogr. 10 poz.

Twórcy

autor

Accardi, L.

• Centro Vito Volterra, Universitá di Roma TorVergata, Via di TorVergata, 00133 Rorna, Italy,

autor

Boukas, A.

• Department of Mathematics, American College of Greece, Aghia Paraskevi, Athens 15342, Greece,

Bibliografia

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• [2] L. Accardi, A mathematical theory of quantum noise, in: Proceedings of the 1st World Congress of the Bernoulli Society, Vol. 1, Y. Prohorov and V. Sazanov (Eds.), VNU Science, 1987, pp. 427-444.
• [3] L. Accardi and A. Boukas, Unitarity conditions for stochastic differential equations driven by non-linear quantum noise, Random Oper. and Stoch. Equations 10 (1) (2002), pp. 1-12.
• [4] L. Accardi, F. Fagnola and J. Quagebeur, Representation free quantum stochastic calculus, J. Funct. Anal. 104 (1992), pp. 140-197.
• [5] L. Accardi, Y. G. Lu and N. Obata, Towards a non-linear extension of stochastic calculus, Publications of the Research Institute for Mathematical Sciences, Kyoto, RIMS Kokyuroku 957, N. Obata (Ed.), 1996, pp. 1-15.
• [6] L. Accardi, Y. G. Lu and I. Yolovich, White noise approach to stochastic calculus and nonlinear Itô tables, submitted to Nagoya Math. J.
• [7] L. Accardi and I. Volovich, Quantum white noise with singular non-linear interaction, to appear.
• [8] F. Fagnola, On quantum stochastic differential equations with unbounded coefficients, Probab. Theory Related Fields 86 (1990), pp. 501-516.
• [9] R. L. Hudson and K. R. Parthasarathy, Quantum Itô’s formula and stochastic evolutions, Comm. Math. Phys. 93 (1984), pp. 301-323.
• [10] K. R. Parthasarathy, An Introduction to Quantum Stochastic Calculus, Birkhäuser Boston Inc., 1992.