A Schrödinger random operator with semimartingale potential
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Jonathan J. Gutierrez-Pavón
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Carlos G. Pacheco
Abstract
We study a Schrödinger random operator where the potential is in terms of a continuous semimartingale. Our model is a generalization of the well-known case where the potential is the white-noise. Our approach is to analyze the random operator by means of its bilinear form. This allows us to construct an inverse operator using an explicit Green kernel. To characterize such homogeneous solutions we use certain stochastic equations in terms of stochastic integrals with respect to the semimartingale. An important tool that we use is the multi-dimensional Itô formula. Also, one important corollary of our results is that the operator has a discrete spectrum.
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Generalized backward stochastic differential equations with jumps in a general filtration
- A Schrödinger random operator with semimartingale potential
- Fractional neutral functional differential equations driven by the Rosenblatt process with an infinite delay
- Modified information criterion for detecting changes in skew slash distribution
- Stability results for stochastic differential equations driven by an additive fractional Brownian sheet
- Delay BSDEs driven by fractional Brownian motion
- Generalized double Lindley distribution: A new model for weather and financial data
Artikel in diesem Heft
- Frontmatter
- Generalized backward stochastic differential equations with jumps in a general filtration
- A Schrödinger random operator with semimartingale potential
- Fractional neutral functional differential equations driven by the Rosenblatt process with an infinite delay
- Modified information criterion for detecting changes in skew slash distribution
- Stability results for stochastic differential equations driven by an additive fractional Brownian sheet
- Delay BSDEs driven by fractional Brownian motion
- Generalized double Lindley distribution: A new model for weather and financial data
