General path integrals and stable SDEs

  • Samuel Baguley

    University of Mannheim B, Germany
  • Leif Döring

    University of Mannheim B, Germany
  • Andreas Kyprianou

    University of Warwick, Coventry, UK
General path integrals and stable SDEs cover
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Abstract

The theory of one-dimensional stochastic differential equations driven by Brownian motion is classical and has been largely understood for several decades. For stochastic differential equations with jumps the picture is still incomplete, and even some of the most basic questions are only partially understood. In the present article we study existence and uniqueness of weak solutions to

driven by a two-sided -stable Lévy process, in the spirit of the classical Engelbert–Schmidt time-change approach. Extending and completing results of Zanzotto we derive a complete characterisation for existence and uniqueness of weak solutions for . Our approach is not based on classical stochastic calculus arguments but on the general theory of Markov processes. We prove integral tests for finiteness of path integrals under minimal assumptions.

Cite this article

Samuel Baguley, Leif Döring, Andreas Kyprianou, General path integrals and stable SDEs. J. Eur. Math. Soc. 26 (2024), no. 9, pp. 3243–3286

DOI 10.4171/JEMS/1331