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Joint Distribution of the Process and its Sojourn Time on the Positive Half-Line for Pseudo-Processes Governed by High-Order Heat Equation

   
@article{EJP782,
	author = {Aimé Lachal and Valentina Cammarota},
	title = {Joint Distribution of the Process and its Sojourn Time on the Positive Half-Line for Pseudo-Processes Governed by High-Order Heat Equation},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {15},
	year = {2010},
	keywords = {pseudo-process, joint distribution of the process and its sojourn time, Spitzer's identity.},
	abstract = {Consider the high-order heat-type equation $\partial_t u=\pm \partial^n_x u$ for an integer $n>2$ and introduce the related Markov pseudo-process $(X(t))_{t\geq0}$. In this paper, we study the sojourn time $T(t)$ in the interval $[0,+\infty)$ up to a fixed time $t$ for this pseudo-process. We provide explicit expressions for the joint distribution of the couple $(T(t),X(t))$.},
	pages = {no. 28, 895-931},
	issn = {1083-6489},
	doi = {10.1214/EJP.v15-782},    
        url = {http://ejp.ejpecp.org/article/view/782}}