From Pseudorandom Walk to Pseudo‐Brownian Motion: First Exit Time from a One‐Sided or a Two‐Sided Interval

A Lachal - International Journal of Stochastic Analysis, 2014 - Wiley Online Library
Let N be a positive integer, ca positive constant and (ξn) n≥ 1 be a sequence of
independent identically distributed pseudorandom variables. We assume that the ξn's take …

A survey on the pseudo-process driven by the high-order heat-type equation concerning the hitting and sojourn times

A Lachal - Methodology and Computing in Applied Probability, 2012 - Springer
Fix an integer N> 2 and let X=(X (t)) t≥ 0 be the pseudo-process driven by the high-order
heat-type equation ∂/∂t=±∂^N\!/∂x^N. The denomination “pseudo-process” means that X …

Pseudoprocesses on a circle and related Poisson kernels

E Orsingher, B Toaldo - … An International Journal of Probability and …, 2015 - Taylor & Francis
Pseudoprocesses, constructed by means of the solutions of higher-order heat-type
equations, have been developed by several authors and many related functionals have …

[HTML][HTML] First exit time from a bounded interval for pseudo-processes driven by the equation∂/∂ t=(− 1) N− 1∂ 2N/∂ x2N

A Lachal - Stochastic Processes and their Applications, 2014 - Elsevier
Let N be an integer greater than 1. We consider the pseudo-process X=(X t) t≥ 0 driven by
the high-order heat-type equation∂/∂ t=(− 1) N− 1∂ 2 N/∂ x 2 N. Let us introduce the first …

First exit time from a bounded interval for pseudo-processes driven by the equation

A Lachal - arXiv preprint arXiv:1402.1825, 2014 - arxiv.org
Let $ N $ be a positive integer. We consider pseudo-Brownian motion $ X=(X (t)) _ {t\ge 0} $
driven by the high-order heat-type equation $\partial/\partial t=(-1)^{N-1}\partial^{2N}/\partial …

A survey on the pseudo-process driven by the high-order heat-type equation concerning the first hitting times and sojourn times

A Lachal - arXiv preprint arXiv:1309.5563, 2013 - arxiv.org
Fix an integer n> 2 and let $(X (t)) _ {t\ge 0} $ be the pseudo-process driven by the high-
order heat-type equation $\partial/\partial t=\pm\partial^ N/\partial x^ N $. The denomination" …

Even-order pseudoprocesses on a circle and related Poisson kernels

E Orsingher, B Toaldo - arXiv preprint arXiv:1212.5786, 2012 - arxiv.org
Pseudoprocesses, constructed by means of the solutions of higher-order heat-type
equations have been developed by several authors and many related functionals have been …

[PDF][PDF] Partial differential equations related to time-changed processes and pseudoprocesses

B Toaldo - 2014 - iris.uniroma1.it
Partial differential equations related to time-changed processes and pseudoprocesses Bruno
Toaldo Page 1 Dottorato di Ricerca in Statistica Metodologica Tesi di Dottorato XXVI Ciclo …

[PDF][PDF] A survey on the pseudo-process driven by the high-order heat-type equation∂/∂ t= 소∂ N/∂ xN concerning the first hitting times and sojourn times

A Lachal - hal.science
Fix an integer N> 2 and let X=(X (t)) t≥ 0 be the pseudo-process driven by the high-order
heat-type equation∂/∂ t=±∂ N/∂ xN. The denomination “pseudo-process” means that X is …

A Review on Time-Changed Pseudoprocesses and Related Distributions

E Orsingher - Modern Stochastics and Applications, 2013 - Springer
Pseudoprocesses governed by higher-order heat-type equations are considered, and a
probabilistic representation of their densities is presented. The composition of …