In this paper, we show that the calibration to an implied volatility surface and the pricing of contingent claims can be as simple in a jump-diffusion framework as in a diffusion one. Indeed, after defining the jump densities as those of diffusions sampled at independent and exponentially distributed random times, we show that the forward and backward Kolmogorov equations can be transformed int...

Abstract We have created a functional framework for class of non-metric gradient systems. The state space is nonnegative measures, and the systems includes Forward Kolmogorov equations laws Markov jump processes on Polish spaces. This comprises definition notion solutions, method to prove existence, an archetype uniqueness result. do this by using only structure that provided directly dissipati...

This paper surveys some results in stochastic differential delay equations beginning with ”On stationary solutions of a stochastic differential equations” by K. Ito and M. Nisio, 1964, and also some results in stochastic stability beginning with the ”Stability of positive supermartingales” by R. Bucy, 1964. The problems discussed in this survey are the existence and uniqueness of solutions of s...

We study a class of discrete-state Markovian models of evolutionary population dynamics for k types of organisms, called discrete evolutionary birth-death processes (EBDP). The organisms in a model environment interact with each other by playing a certain game. Birth rates for type i organisms at time t are determined by their expected payoff in the game against an opponent chosen randomly from...

We consider a nonlinear stochastic differential equation driven by an $$\alpha $$ -stable Lévy process ( $$1<\alpha <2$$ ). first prove existence and uniqueness of the invariant measure Bogoliubov-Krylov argument. Then we obtain some regularity results for probability density its establishing priori estimate corresponding stationary Fokker-Planck equation. Finally, Kolmogorov backward perturbat...

ABSTRACT This paper deals with availability optimization for screw plant using genetic algorithm. Screw plant has four main subsystems, out of theses four subsystems, two subsystems are provided with cold stand by alternativeConsidering the exponential distribution for the probable failures and repairs, Mathematical formulation of the problem is done using probabilistic approach and differentia...

This paper deals with the mathematical modeling and performance optimization for the paper making system in a paper plant using Genetic Algorithm. The paper making system of a paper plant has four main subsystems, arranged in series and parallel. Considering exponential distribution for the probable failures and repairs, the mathematical formulation of the problem is done using probabilistic ap...

This paper deals with the performance analysis of the screening unit in a paper plant using Genetic Algorithm. The screening unit in the paper plant has four main subsystems. These subsystems are arranged in series and parallel configurations. Considering exponential distribution for the probable failures and repairs, the mathematical formulation of the problem is done by Markov birth-death pro...

Motivated by applications to proving regularity of solutions to degenerate parabolic equations arising in population genetics, we study existence, uniqueness and the strong Markov property of weak solutions to a class of degenerate stochastic differential equations. The stochastic differential equations considered in our article admit solutions supported in the set [0,∞)×R, and they are degener...

in this article differential transformation method (dtms) has been used to solve neutral functional-differential equations with proportional delays. the method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. exact solutions can also be obtained from the kno...