Probability law, flow function, maximum distribution of wave-governed random motions and their connections with Kirchoff's laws

Orsingher, Enzo

doi:10.1016/0304-4149(90)90056-x

Cited by 140 publications

(126 citation statements)

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“…For the purpose, we recall some results on the so-called telegraph processes [135][136][137][138]. After this short review, we shall make the connection with multiscale quantum spacetimes apparent.…”

Section: B Fractional Telegraph Processmentioning

confidence: 99%

Diffusion in multiscale spacetimes

Calcagni

2013

Phys. Rev. E

140

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We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are partly based on the literature in probability and percolation theory but their physical interpretation here is different since they apply to quantum spacetime itself. The case of multiscale (in particular, multifractal) spacetimes is then considered through a number of examples, and the most general spectral-dimension profile of multifractional spaces is constructed.

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Section: B Fractional Telegraph Processmentioning

confidence: 99%

Diffusion in multiscale spacetimes

Calcagni

2013

Phys. Rev. E

140

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“…In some sense, the above and the following result integrate Section 3 of Orsingher [17]. It is trivially true that the odd moments of the telegraph process are all zero, hence we present the formula for the moments of even order.…”

Section: Moments Of the Telegraph Processmentioning

confidence: 74%

“…the distribution of X(t), is a mixture of continuous and discrete components. This distribution has been obtained by Goldstein [8], Orsingher [17], and Pinsky [18] with different techniques. The transition density is given by …”

Section: Moments Of the Telegraph Processmentioning

confidence: 93%

“…2λ (see Orsingher [17]). Di Crescenzo and Martinucci [3] derived the moment generating function for the telegraph process; i.e., for all s ∈ R and t ≥ 0,…”

Section: Moments Of the Telegraph Processmentioning

confidence: 99%

“…Many authors analyzed probabilistic properties of the process over the years (see e.g. Orsingher [16] and [17]; Pinsky [18]; Fong and Kanno [7]; Stadje and Zacks [21]). Di Crescenzo and Pellerey [4] proposed the geometric telegraph process as a model to describe the dynamics of the price of risky assets, i.e.…”

Section: Introductionmentioning

confidence: 99%

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Estimation for the discretely observed telegraph process

Iacus

Yoshida

2009

Theor. Probability and Math. Statist.

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Abstract. The telegraph process {X(t), t > 0} is supposed to be observed at n + 1 equidistant time points t i = i∆ n , i = 0, 1, . . . , n. The unknown value of λ, the underlying rate of the Poisson process, is a parameter to be estimated. The asymptotic framework considered is the following: ∆ n → 0, n∆ n = T → ∞ as n → ∞. We show that previously proposed moment type estimators are consistent and asymptotically normal but not efficient. We study further an approximated moment type estimator which is still not efficient but comes in explicit form. For this estimator the additional assumption n∆ 3 n → 0 is required in order to obtain asymptotic normality. Finally, we propose a new estimator which is consistent, asymptotically normal and asymptotically efficient under no additional hypotheses.

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Stochastic Processes

2011

Option Pricing and Estimation of Financial Models With R

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Probability law, flow function, maximum distribution of wave-governed random motions and their connections with Kirchoff's laws

Cited by 140 publications

References 4 publications

Diffusion in multiscale spacetimes

Diffusion in multiscale spacetimes

Estimation for the discretely observed telegraph process

Stochastic Processes

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