Showing papers by "Enzo Orsingher published in 2018"
TL;DR: In this article, an integro-differential form of the Kolmogorov's backward equations for a large class of homogeneous semi-Markov processes, having the form of an abstract Volterra integrodifferential equation, was provided.
21 citations
01 Jan 2018
TL;DR: In this paper, the authors show connections between special functions arising from generalized Conway-Maxwell-Poisson type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators.
Abstract: In this paper, we show several connections between special functions arising from generalized Conway-Maxwell-Poisson (COM-Poisson) type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators. New analytical results are obtained, showing the particular role of Hadamard-type derivatives in connection with a recently introduced generalization of the Le Roy function. We are also able to prove a general connection between fractional hyper-Bessel-type equations involving Hadamard operators and Le Roy functions.
21 citations
TL;DR: In this paper, the authors considered the random initial conditions given by harmonizable sub-Gaussian processes and obtained bounds for the distributions of the suprema over bounded and unbounded domains for solutions of higher-order heat-type equations.
Abstract: In the present paper we continue the investigation of solutions to higher-order heat-type equations with random initial conditions, which play the important role in many applied areas. We consider the random initial conditions given by harmonizable $\varphi$-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema over bounded and unbounded domains for solutions of such equations. The results obtained in the paper hold, in particular, for the case of Gaussian initial condition.
9 citations
TL;DR: In this article, the authors considered the random initial conditions given by harmonizable -sub-Gaussian processes and obtained bounds for the distributions of the suprema over bounded and unbounded domains for solutions of higher-order heat-type equations.
Abstract: In the present paper we continue the investigation of solutions to higher-order heat-type equations with random initial conditions, which play the important role in many applied areas. We consider the random initial conditions given by harmonizable $$\varphi $$
-sub-Gaussian processes. The main results are the bounds for the distributions of the suprema over bounded and unbounded domains for solutions of such equations. The results obtained in the paper hold, in particular, for the case of Gaussian initial condition.
9 citations
19 Sep 2018
TL;DR: In this article, fractional equations governing the distribution of reflecting drifted Brownian motions are presented in terms of tempered Riemann-Liouville type derivatives, and a Marchaud-type form is obtained and a Riesz tempered fractional derivative is examined, together with its Fourier transform.
Abstract: Fractional equations governing the distribution of reflecting drifted Brownian motions are presented. The equations are expressed in terms of tempered Riemann--Liouville type derivatives. For these operators a Marchaud-type form is obtained and a Riesz tempered fractional derivative is examined, together with its Fourier transform.
4 citations
TL;DR: In this paper, fractional equations governing the distribution of reflecting drifted Brownian motions are presented in terms of tempered Riemann-Liouville type derivatives, and a Marchaud-type form is obtained and a Riesz tempered fractional derivative is examined, together with its Fourier transform.
Abstract: Fractional equations governing the distribution of reflecting drifted Brownian motions are presented. The equations are expressed in terms of tempered Riemann--Liouville type derivatives. For these operators a Marchaud-type form is obtained and a Riesz tempered fractional derivative is examined, together with its Fourier transform.
3 citations
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TL;DR: In this article, the authors derived the last zero crossing distribution of the drifted Brownian motion with drift and the first passage time through the zero level of a Brownian Motion with drift.
Abstract: In this paper we consider the iterated Brownian motion $ ^{\mu_1}_{\mu_2}\!I(t) = B_1^{\mu_1} ( | B_{2}^{\mu_2} (t)|) $ where $B_j^{\mu_j} , j=1,2$ are two independent Brownian motions with drift $\mu_j$. Here we study the last zero crossing of $ ^{\mu_1}_{\mu_2}\!I(t) $ and for this purpose we derive the last zero-crossing distribution of the drifted Brownian motion. We derive also the joint distribution of the last zero crossing before $ t $ and of the first passage time through the zero level of a Brownian motion with drift $ \mu $ after $ t $. All these results permit us to derive explicit formulas for ${^I_\mu T_0} = \sup \{ s < \max_{0\leq z\leq t} |B_2(z)| : B_1^\mu (s) = 0 \}$. Also the iterated zero-crossing $ {^{\mu_1} T}_{0, {^{\mu_2} T}_{0,t}} $ is analyzed and extended to the case where the level of nesting is arbitrary.
1 citations