Projects per year
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 dZt=σ(Zt−)dXt
driven by a two-sided α-stable L´evy 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 α∈(0,1). Our approach is not based on classical stochasticcal culus arguments but on the general theory of Markov processes. We prove integral tests for finiteness of path integrals under minimal assumptions. Keywords: Stochastic Differential Equations, stable processes, Markov processes, perpetuities, time change.
driven by a two-sided α-stable L´evy 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 α∈(0,1). Our approach is not based on classical stochasticcal culus arguments but on the general theory of Markov processes. We prove integral tests for finiteness of path integrals under minimal assumptions. Keywords: Stochastic Differential Equations, stable processes, Markov processes, perpetuities, time change.
Original language | English |
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Journal | Journal of the European Mathematical Society |
DOIs | |
Publication status | Published - 1 Jun 2023 |
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Dive into the research topics of 'General path integrals and stable SDEs'. Together they form a unique fingerprint.Projects
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Real-Valued Self-Similar Markov Processes and their Applications
Kyprianou, A. (PI)
Engineering and Physical Sciences Research Council
2/06/14 → 1/10/17
Project: Research council