In this paper we propose a new homogeneous stochastic Gompertz diffusion model with a threshold parameter. This can be considered an extension of the homogeneous three parameter Gompertz process with the addition of a fourth parameter. From the corresponding Kolmogorov equations and Ito’s stochastic differential equations, we obtain the transition probability density function and the moments of...

Aim. The paper aims to develop an algorithm that would allow finding the required number of items (SPTA) for a complex system, whose elements may or not be maintainable. Methods. Markov models were used describing system. final probabilities obtained using Kolmogorov equation. system equations has stationary solution. Classical methods probability theory and mathematical dependability used. Con...

Abstract. We study the asymptotic behavior of solutions to stochastic evolution equations with monotone drift and multiplicative Poisson noise in the variational setting, thus covering a large class of (fully) nonlinear partial differential equations perturbed by jump noise. In particular, we provide sufficient conditions for the existence, ergodicity, and uniqueness of invariant measures. Furt...

Seasonal changes in temperature, humidity, and rainfall affect vector survival emergence of mosquitoes thus impact the dynamics vector-borne disease outbreaks. Recent studies deterministic stochastic epidemic models with periodic environments have shown that average basic reproduction number is not sufficient to predict an outbreak. We extend these time-nonhomogeneous dengue demographic variabi...

Abstract. A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), i(t), Y (t)) on (T × {1, 2} × R), where T is the twodimensional torus. Here (K(t), i(t)) is an autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance. Y (t) is an additive functional of K, define...

We prove pathwise uniqueness for stochastic differential equations driven by non-degenerate symmetric α-stable Lévy processes with values in Rd having a bounded and β-Hölder continuous drift term. We assume β > 1− α/2 and α ∈ [1, 2). The proof requires analytic regularity results for the associated integro-differential operators of Kolmogorov type. We also study differentiability of solutions w...

The existence of a moment function satisfying a drift function condition is well-known to guarantee non-explosiveness of the associated minimal Markov process (cf.[1, 6]), under standard technical conditions. Surprisingly, the reverse is true as well for a countable space Markov process. We prove this result by showing that recurrence of an associated jump process, that we call the α-jump proce...

In this paper we study stochastic models for the transport of particles in a uidized bed reactor, and compute the associated residence time distribution (RTD). Our main model is basically a diiusion process in 0; A] with reeecting/absorbing boundary conditions, modiied by allowing jumps to the origin as a result of transport of particles in the wake of rising uidization bubbles. We study discre...

Estimation of parameters in the drift and diffusion terms of stochastic differential equations involves simulation and generally requires substantial data sets. We examine a method that can be applied when available time series are limited to less than 20 observations per replication. We compare and contrast parameter estimation for linear and nonlinear firstorder stochastic differential equati...

1 Basic aspects of continuous time Markov chains 3 1.1 Markov property . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Regular jump chain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Holding times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Poisson process . . . . . . . . . . . . . . ....