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September 1, 2013
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August 3, 2013
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Abstract. Let be an ℝ d -valued càdlàg random process, and let F be an increasing from zero ℝ-valued random process whose values at all times are measurable w.r.t. some σ-algebra (the class of all such processes is denoted by ). Conditions guaranteing that for every bounded continuous function are found. In the most general theorem they are formulated in terms of F and . Further we consider the case when satisfies an equation of the kind where is an -measurable random variable, is a continuous process of class , A is a matrix-valued random process -measurable in , and S is an ℝ d -valued semimartingale with conditionally on independent increments and initial value 0. In this case, sufficient conditions for () are stated in terms of F and the constituents of the equation. Besides, the characteristic function of an n -dimensional distribution of is found.
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August 3, 2013
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Abstract. We present Feynman–Kac path integrals representations for scalar wave motions on variable medium. The main new points on them is about their rigorous mathematical validity on the space of continuous functions vanishing at infinity, besides of possessing intrinsically the physical property of causal wave field propagation, thus solving mathematically the long standing problem on the subject of automatically leading to causality wave propagation.
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July 30, 2013
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Abstract. Motivated by the Gaussian channel models, we calculate the mutual information for processes described by multidimensional stochastic differential equations driven by sub-fractional Brownian motion.
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August 20, 2013
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Abstract. We estimate the parameters of a nonstationary multivariate ARFIMA (AutoRegressive Fractionally Integrated Moving Average) process by the quasi likelihood approach. Then, we define the pseudo-spectral density of the process. Under some assumptions, we establish consistency, asymptotic normality.