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Exponential Behaviour of Nonlinear Fractional Schrödinger Evolution Equation with Complex Potential and Poisson Jumps

Author

Listed:
  • N. Durga

    (Vellore Institute of Technology)

  • P. Muthukumar

    (The Gandhigram Rural Institute (Deemed to be University))

Abstract

This paper aims to investigate stochastic fractional Schrödinger evolution equations with potential and Poisson jumps in Hilbert space. The solvability of the proposed system is established by using fractional calculus, semigroup theory, Krasnoselskii’s fixed point theorems and stochastic analysis. Furthermore, sufficient conditions are formulated and proved to assure that the mild solution decays exponentially to zero in the square mean. Lastly, an application is given to demonstrate the developed theory.

Suggested Citation

  • N. Durga & P. Muthukumar, 2023. "Exponential Behaviour of Nonlinear Fractional Schrödinger Evolution Equation with Complex Potential and Poisson Jumps," Journal of Theoretical Probability, Springer, vol. 36(4), pages 1939-1955, December.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:4:d:10.1007_s10959-023-01266-5
    DOI: 10.1007/s10959-023-01266-5
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    References listed on IDEAS

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    1. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," The Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
    2. Ge, Fudong & Kou, Chunhai, 2015. "Stability analysis by Krasnoselskii’s fixed point theorem for nonlinear fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 308-316.
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