Scholarlink

<p>The generalized convolution is certain operation on the set of probability measures. It is defined by K. Urbanik (see [K. Urbanik, Generalized convolutions, <i>Stud. Math.</i>, 23:217–245 1964], [J.K. Misiewicz, K. Oleszkiewicz, and K. Urbanik, Classes of measures closed under mixing and convolution. Weak stability, <i>Stud. Math.</i>, 167(3):195–213, 2005], and [B.H. Jasiulis, Limit property for regular and weak generalized convolutions, <i>J. Theor. Probab.</i>, 23(1):315–327, 2010]). They allow us to define and study the infinite divisibility of probability measures and to construct Lévy processes in the sense of generalized convolutions. This approach was undertaken in [M. Borowiecka-Olszewska, B.H. Jasiulis-Gołdyn, J.K. Misiewicz, and J. Rosiński, Lévy Processes and stochastic integrals in the sense of generalized convolutions, <i>Bernoulli</i>, 21(4):2513–2551, 2015]. It turned out that Lévy processes with respect to generalized convolutions are Markov in the classical sense. Of course, Markov processes are not necessarily Lévy. In this paper, we investigate the converse: when Markov processes are Lévy in the sense of some generalized convolution?</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Markov processes generated by generalized convolutions

  • 期刊论文

  • 发表日期：

    2026年4月1日

查看全文
  • Jolanta Krystyna Misiewicz,
  • Jan Rosiński

摘要

The generalized convolution is certain operation on the set of probability measures. It is defined by K. Urbanik (see [K. Urbanik, Generalized convolutions, Stud. Math., 23:217–245 1964], [J.K. Misiewicz, K. Oleszkiewicz, and K. Urbanik, Classes of measures closed under mixing and convolution. Weak stability, Stud. Math., 167(3):195–213, 2005], and [B.H. Jasiulis, Limit property for regular and weak generalized convolutions, J. Theor. Probab., 23(1):315–327, 2010]). They allow us to define and study the infinite divisibility of probability measures and to construct Lévy processes in the sense of generalized convolutions. This approach was undertaken in [M. Borowiecka-Olszewska, B.H. Jasiulis-Gołdyn, J.K. Misiewicz, and J. Rosiński, Lévy Processes and stochastic integrals in the sense of generalized convolutions, Bernoulli, 21(4):2513–2551, 2015]. It turned out that Lévy processes with respect to generalized convolutions are Markov in the classical sense. Of course, Markov processes are not necessarily Lévy. In this paper, we investigate the converse: when Markov processes are Lévy in the sense of some generalized convolution?