The renewal equation in nonlinear approximation

The family of Markov processes are considered in the article. We study the multidimensional renewal equation in nonlinear approximation. The purpose of the work is to find the limit of renewal function.

Renewal function asymptotics refined à la Feller

RENEWAL FUNCTION ASYMPTOTICS REFINED À LA FELLERFeller’s volume 2 shows how to use the Key Renewal Theorem to prove that in the limit x!1, the renewal function Ux of a renewal process with nonarithmetic generic lifetime X with finite mean EX=1=and second moment differs from its linear asymptote x by the quantity 122EX2. His first edition 1966 but not the second in 1971 asserted that a similar approach would refine this asymptotic result when X has finite higher order moments. The paper shows how higher order moments may justify drawing conclusions from a recurrence relation that exploits a general renewal equation and further appeal to the Key Renewal Theorem.

How To Combine Ozone Therapies With Other Modalities For Maximum Efficacy

In order to use Bio-Oxidative Therapies effectively, a small shift in thinking is needed. One needs to shift from Disease Literacy to Healing Literacy This shift in thinking leads to the inevitable conclusion that: Impaired Oxygen Signaling is the common denominator for all disease. Impaired Oxygen Signaling affects: • O2 driven energetics • O2's detergent function • O2's cellular repair function • O2's renewal function It is important to be aware of Oxygen's multiple functions in order to appreciate the importance of the role bio-oxidative therapies play in the reversal of disease conditions. In fact, no treatment of chronic disease can be complete without addressing ALL Oxygen-related issues relevant to a particular patient. What are these oxygen related issues that need to be addressed? There are 4 distinct steps that lead to disease manifestation linked to Oxygen: · Dysfunctional Oxygen Metabolism · Acidosis · Oxidative Coagulation · Oxidized Lymph Once the above conditions are understood, it becomes clear that combining bio-oxidative therapies with other modalities can improve the outcome of those modalities. Examples of how to combine therapies to create effective protocols for improved clinical outcome will be discussed. In Summary: A clear understanding of the Oxygen Model of Disease will enable the practitioner to customize and create innovative combinations for the individual patient.