On stability of the Markov-modulated skew CIR process

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• 作者：Guangli Xu^a ; ^{xuguangli@mail.nankai.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Yongjin Wang^a ; ^b ; ^{yjwang@nankai.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Skew CIR ; Markov-modulated ; Stationary distribution
• 刊名：Statistics & Probability Letters
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：109
• 期：Complete
• 页码：139-144
• 全文大小：371 K

文摘

In this paper we consider the stability of a skew Cox–Ingersoll–Ross (CIR) process class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167715215003739&_mathId=si1.gif&_user=111111111&_pii=S0167715215003739&_rdoc=1&_issn=01677152&md5=6eef7e0784375d39ec142961d40da366" title="Click to view the MathML source">{X_t}_t⩾0class="mathContainer hidden">class="mathCode">msub>{<msub>Xtmsub>}t⩾0msub> whose parameters depend on a finite-state and irreducible continuous-time Markov chain class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167715215003739&_mathId=si2.gif&_user=111111111&_pii=S0167715215003739&_rdoc=1&_issn=01677152&md5=aaa34eca722cfcd98636068d9741b4fa" title="Click to view the MathML source">{J_t}_t⩾0class="mathContainer hidden">class="mathCode">msub>{<msub>Jtmsub>}t⩾0msub>. First, we prove the existence and uniqueness of the bivariate process class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167715215003739&_mathId=si3.gif&_user=111111111&_pii=S0167715215003739&_rdoc=1&_issn=01677152&md5=ce56d1077fb3532e1d35ef72abf8b792" title="Click to view the MathML source">{(X_t,J_t)}_t⩾0class="mathContainer hidden">class="mathCode">msub>{(<msub>Xtmsub>,<msub>Jtmsub>)}t⩾0msub> and derive the corresponding infinitesimal generator. Then we provide the stationary distribution equation of this bivariate process through their infinitesimal generator and as special cases, the explicit stationary distributions when class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0167715215003739&_mathId=si4.gif&_user=111111111&_pii=S0167715215003739&_rdoc=1&_issn=01677152&md5=8446b1a5b792c3fe9d000b13527776ab" title="Click to view the MathML source">J_tclass="mathContainer hidden">class="mathCode">msub>Jtmsub> has two or one state are calculated in the end.