In this paper, we investigate the exact controllability properties of an advection-diffusion equation on a bounded domain, using timeand space-dependent velocity fields as the control parameters. This partial differential equation (PDE) is the Kolmogorov forward equation for a reflected diffusion process that models the spatiotemporal evolution of a swarm of agents. We prove that if a target pr...

This thesis is focused around weak convergence analysis of approximations of stochastic evolution equations in Hilbert space. This is a class of problems, which is sufficiently challenging to motivate new theoretical developments in stochastic analysis. The first paper of the thesis further develops a known approach to weak convergence based on techniques from the Markov theory for the stochast...

The nonlinear dynamics of biochemical reactions in a small-sized system on the order of a cell are stochastic. Assuming spatial homogeneity, the populations of n molecular species follow a multi-dimensional birth-and-death process on Z . We introduce the Delbrück–Gillespie process, a continuous-time Markov jump process, whose Kolmogorov forward equation has been known as the chemical master equ...

semilinear stochastic evolution equations with multiplicative l'evy noise are considered‎. ‎the drift term is assumed to be monotone nonlinear and with linear growth‎. ‎unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎we establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎as corollarie...

We consider a signal process X taking values in a complete, separable metric space E. X is assumed to be a Markov process charachterized via the martingale problem for an operator A. In the context of the finitely additive white noise theory of filtering, we show that the optimal filter Γt(y) is the unique solution of the analogue of the Zakai equation for every y, not necessarily continuous. T...

The present paper deals with development of a simulation model for the performance evaluation of feed water system of a thermal power plant using Markov Birth-Death process and probabilistic approach. In present paper, the feed water system consists of four subsystems. After drawing transition diagram for feed water system, differential equations are developed and then solved recursively using ...

Abstract Stationary distributions of Markov processes can typically be characterized as probability measures that annihilate the generator in the sense that ∫ E Afdμ = 0 for f ∈ D(A); that is, for each such μ, there exists a stationary solution of the martingale problem for A with marginal distribution μ. This result is extended to models corresponding to martingale problems that include absolu...

This paper explicitly computes the transition densities of a spectrally negative stable process with index greater than one, reflected at its infimum. First we derive the forward equation using the theory of sun-dual semigroups. The resulting forward equation is a boundary value problem on the positive half-line that involves a negative Riemann-Liouville fractional derivative in space, and a fr...

This work investigates the dynamics of competitive Kolmogorov systems formulated in a semi-Markov regime-switching framework. The conditional holding time each environmental regime is allowed to follow arbitrary probability distribution on nonnegative half-line sense approximations. Sharp sufficient conditions coexistence and exclusion species are established, case ...

In a recent paper [16], one of us identified all of the quasi-stationary distributions for a non-explosive, evanescent birth-death process for which absorption is certain, and established conditions for the existence of the corresponding limiting conditional distributions. Our purpose is to extend these results in a number of directions. We shall consider separately two cases depending on wheth...