 The object of the present study is to propose the power law process also known as non homogenous poison process which is identical to the weibull process in analyzing and modeling different types of cancer, especially breast cancer.  The key objective is to study the change of the tumor growth as a function of age. The intensity function within the power law process will give us the rate of ...

Let (Mt )0≤t≤1 be a continuous martingale with initial law M0 ∼ μ0, and terminal law M1 ∼ μ1, and let S = sup0≤t≤1Mt . In this paper we prove that there exists a greatest lower bound with respect to stochastic ordering of probability measures, on the law of S. We give an explicit construction of this bound. Furthermore a martingale is constructed which attains this minimum by solving a Skorokho...

In this paper we consider the winding number, θ(s), of planar Brownian motion and study asymptotic behavior of the process of the maximum time, the time when θ(s) attains the maximum in the interval 0 ≤ s ≤ t. We find the limit law of its logarithm with a suitable normalization factor and the upper growth rate of the maximum time process itself. We also show that the process of the last zero ti...

is obvious, and then what always hold in the Mamdani's case is the equivalence (p 2 q ! r) = (p ! r) ^ (q ! r): (14) Consequently, if I is a Mamdani–Larsen's implication (8) never holds, but (14) is always true. IV. CONCLUSION After remembering the four main types of implications used in Fuzzy Logic, the equality [p ^ q ! r] = [(p ! r) _ (q ! r)] (*) is analyzed bot in complemented lattices and...