Here we will present some deeper results in renewal theory such as a central limit theorem for counting processes, stationary versions of renewal processes, renewal equations, the key renewal theorem, weak convergence. 1 Central limit theorem for counting processes Consider a renewal process {t n : n ≥ 1} with iid interarrival times X n = t n − t n−1 , n ≥ 0, such that 0 < E(X) = 1/λ < ∞ and 0 ...

Methods of estimating unknown parameters of a trend function for trend-renewal processes are investigated in the case when the renewal distribution function is unknown. If the renewal distribution is unknown, then the likelihood function of the trend-renewal process is unknown and consequently the maximum likelihood method cannot be used. In such a situation we propose three other methods of es...

stem cells are generally defined as clonogenic cells capable of both self-renewal and differentiation. probably the best method for long-term preservation of spermatogonial stem cells is cryopreservation. in this study, effects of follicle stimulating hormone and testosterone on viability rate of cryopreserved spermatogonial stem cell after thawing were investigated. sertoli and spermatogonial ...

Uncertain renewal process is an important uncertain process. This paper discusses some sample properties of uncertain renewal process. Besides, it gives some theorems on first hitting time of renewal process.

Sustainability is observed in many aspects and elements of traditional Iranian architecture, plannerand landscape architecture, and this method was used to solve many problems for many countries. The aim of thisarticle is to achieve a sustainable approach in planning urban renewal projects to identify the relationship betweenurban design considerations and the sustainable development objectives...

nucleostemin (ns), a stem cell-abundant nucleolar protein, is critical for maintaining the self-renewal and proliferative properties of normal and cancerous stem cells. recent data suggests that ns signaling is important for proliferation of t-cells and leukemia cells. this study was conducted to verify the role of ns in pathogenesis and treatment of t-cell acute lymphocytic leukemia (t-all). o...

Renewal of an extinguished conditioned response has been demonstrated in humans and in animals using various types of procedures, except renewal of motor learning such as eyeblink conditioning. We tested renewal of delay and trace eyeblink conditioning in a virtual environment in an ABA design. Following acquisition in one context (A, e.g., an airport) and extinction in a different context (B, ...

In this article, we study the discounted penalty at ruin in a perturbed compound Poisson model with two-sided jumps. We show that it satisfies a renewal equation under suitable conditions and consider an application of this renewal equation to study some perpetual American options. In particular, our renewal equation gives a generalization of the renewal equation in Gerber and Landry [2] where ...