The Annals of Probability

On the error estimate of the integral kernel for the Trotter product formula for Schrödinger operators

Satoshi Takanobu

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Abstract

The error estimate of the integral kernel for the Trotter product formula for Schrödinger operators is shown. A basic tool for doing so is the Feynman-Kac formula based on the pinned Brownian motion. This formula enables us to express the integral kernel in handleable form and hence estimate it. As a consequence the Trotter product formula in the $L_p$ operator norm is obtained.

Article information

Source
Ann. Probab., Volume 25, Number 4 (1997), 1895-1952.

Dates
First available in Project Euclid: 7 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1023481116

Digital Object Identifier
doi:10.1214/aop/1023481116

Mathematical Reviews number (MathSciNet)
MR1487441

Zentralblatt MATH identifier
0898.60064

Subjects
Primary: 60H30: Applications of stochastic analysis (to PDE, etc.)
Secondary: 60H10 60J35 60J65

Keywords
Trotter product formula in the kernel level Trotter product formula in $L_p$-operator norm Feynman-Kac formula

Citation

Takanobu, Satoshi. On the error estimate of the integral kernel for the Trotter product formula for Schrödinger operators. Ann. Probab. 25 (1997), no. 4, 1895--1952. doi:10.1214/aop/1023481116. https://projecteuclid.org/euclid.aop/1023481116


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References

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