5,981 research outputs found
First hitting time and place, monopoles and multipoles for pseudo-processes driven by the equation
Consider the high-order heat-type equation for an integer and introduce the related
Markov pseudo-process . In this paper, we study several
functionals related to : the maximum and minimum
up to time ; the hitting times and of the half lines
and respectively. We provide explicit expressions
for the distributions of the vectors and , as well
as those of the vectors and .Comment: 51 page
Recoil momentum spectrum in directional dark matter detectors
Directional dark matter detectors will be able to record the recoil momentum
spectrum of nuclei hit by dark matter WIMPs. We show that the recoil momentum
spectrum is the Radon transform of the WIMP velocity distribution. This allows
us to obtain analytic expressions for the recoil spectra of a variety of
velocity distributions. We comment on the possibility of inverting the recoil
momentum spectrum and obtaining the three-dimensional WIMP velocity
distribution from data.Comment: 16 pages, 4 figures, revtex4 (replaced with accepted version, typos
corrected
Subordination Pathways to Fractional Diffusion
The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and
under power law regime is splitted into three distinct random walks: (rw_1), a
random walk along the line of natural time, happening in operational time;
(rw_2), a random walk along the line of space, happening in operational
time;(rw_3), the inversion of (rw_1), namely a random walk along the line of
operational time, happening in natural time. Via the general integral equation
of CTRW and appropriate rescaling, the transition to the diffusion limit is
carried out for each of these three random walks. Combining the limits of
(rw_1) and (rw_2) we get the method of parametric subordination for generating
particle paths, whereas combination of (rw_2) and (rw_3) yields the
subordination integral for the sojourn probability density in space-time
fractional diffusion.Comment: 20 pages, 4 figure
Calculating multivariate ruin probabilities via GaverâStehfest inversion technique.
Multivariate characteristics of risk processes are of high interest to academic actuaries. In such models, the probability of ruin is obtained not only by considering initial reserves u but also the severity of ruin y and the surplus before ruin x. This ruin probability can be expressed using an integral equation that can be efficiently solved using the GaverâStehfest method of inverting Laplace transforms. This approach can be considered to be an alternative to recursive methods previously used in actuarial literatureMultivariate ultimate ruin probability; Laplace transform; Integral equations; Numerical methods;
The M-Wright function in time-fractional diffusion processes: a tutorial survey
In the present review we survey the properties of a transcendental function
of the Wright type, nowadays known as M-Wright function, entering as a
probability density in a relevant class of self-similar stochastic processes
that we generally refer to as time-fractional diffusion processes.
Indeed, the master equations governing these processes generalize the
standard diffusion equation by means of time-integral operators interpreted as
derivatives of fractional order. When these generalized diffusion processes are
properly characterized with stationary increments, the M-Wright function is
shown to play the same key role as the Gaussian density in the standard and
fractional Brownian motions. Furthermore, these processes provide stochastic
models suitable for describing phenomena of anomalous diffusion of both slow
and fast type.Comment: 32 pages, 3 figure
On the fractional Poisson process and the discretized stable subordinator
The fractional Poisson process and the Wright process (as discretization of
the stable subordinator) along with their diffusion limits play eminent roles
in theory and simulation of fractional diffusion processes. Here we have
analyzed these two processes, concretely the corresponding counting number and
Erlang processes, the latter being the processes inverse to the former.
Furthermore we have obtained the diffusion limits of all these processes by
well-scaled refinement of waiting times and jumpsComment: 30 pages, 4 figures. A preliminary version of this paper was an
invited talk given by R. Gorenflo at the Conference ICMS2011, held at the
International Centre of Mathematical Sciences, Pala-Kerala (India) 3-5
January 2011, devoted to Prof Mathai on the occasion of his 75 birthda
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