In this paper we present a comprehensive existence theory for linear and nonlinear reaction random walk systems. The methods are based on semigroup theory for solutions of differential equations on Banach spaces. The solution properties on a bounded domain sensitively depend on the choice of boundary conditions. For Neumann or for periodic boundary conditions, singularities are transported alon...

The article analyzes the relationships between disease, knowledge, and settlement of the Brazilian territory within the context of the Strategic Telegraph Commission from Mato Grosso to Amazonas, more famously known as the Rondon Commission. From 1907 to 1915, the commission traversed broad regions of what are now the states of Mato Grosso, Rondônia and Amazonas as part of its endeavor to set u...

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The problem of parameter estimation is considered for the twostate telegraph process, observed in white Gaussian observation noise. An online one-step Maximum Likelihood Estimator (MLE) process is constructed, using a preliminary Method of Moments (MM) estimator. The obtained estimation procedure is shown to be asymptotically normal and efficient in the large sample regime. MSC 2000 Classificat...

We present a model for the Lagrangian dynamics of inertial particles in a compressible flow, where fluid velocity gradients are modeled by a telegraph noise. The model allows for an analytic investigation of the role of time correlation of the flow in the aggregation-disorder transition of inertial particles. The dependence on the Stokes number St and the Kubo number Ku of the Lyapunov exponent...

We analyse the vector process (X0(t), X1(t), . . . , Xn(t), t > 0) where Xk(t) = t ∫ 0 Xk−1(s)ds, k = 1, . . . , n, and X0(t) is the two-valued telegraph process. In particular, the hyperbolic equations governing the joint distributions of the process are derived and analysed. Special care is given to the case of the process (X0(t), X1(t), X2(t), t > 0) representing a randomly accelerated motio...

Synopsis—The most obvious method for determining the distortion of telegraph signals is to calculate the transients of the telegraph system. This method has been treated by various writers, and solutions are available for telegraph lines with simple terminal conditions. It is well known that the extension of the same methods to more complicated terminal conditions, which represent the usual ter...