Exponential Integrability and Application to Stochastic Quantization

Exponential Integrability and Application to Stochastic Quantization Appl Math Optim 37:295–353 (1998) 1998 Springer-Verlag New York Inc. Exponential Integrability and Application to Stochastic Quantization ¤¤ Y. Hu and G. Kallianpur Center for Stochastic Processes, Department of Statistics, The University of North Carolina at Chapel Hill, 321 Phillips Hall, Chapel Hill, NC 27599-3260, USA Abstract. We study the exponential integrability problem for I . f /, i.e., n n E expf I . f /g < 1, where I . f / is a multiple Ito–W ˆ iener integral on some Gaus- n n n n sian space arising from the constructive quantum field theory and from stochastic quantization. We also study a class of singular infinite-dimensional stochastic dif- ferential equations whose drift coefficients are measurable and unbounded. Using a condition due to Kazamaki, we prove the existence of a weak solution assuming some integrability conditions on the drift coefficient. Then we apply the exponen- tial integrability theorem and the existence theorem to study infinite-dimensional stochastic differential equations of stochastic quantization. Key Words. P.8/ field, Multiple integral, Stochastic quantization, Infinite- dimensional stochastic differential equation, Exponential integrability, Cameron– Martin–Girsanov theorem. AMS Classification. Primary 60H10, 60H15, Secondary 34F05, 60J60, 60K40, 60G20, 81T08. 1. Introduction Let H be a separable http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Exponential Integrability and Application to Stochastic Quantization

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Copyright © Inc. by 1998 Springer-Verlag New York
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
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