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Markov Random Walk Representations with Continuous Distributions
[article]

2012
*
arXiv
*
pre-print

*Representations*based on

*random*

*walks*can exploit discrete data

*distributions*for clustering and classification. We extend such

*representations*from discrete to

*continuous*

*distributions*. ... Transition probabilities are now calculated using a diffusion equation

*with*a diffusion coefficient that inversely depends on the data density. ...

*random*

*walks*We begin by reviewing the discrete

*Markov*

*random*

*walk*

*representation*. ...

##
###
Page 2825 of Mathematical Reviews Vol. , Issue 84g
[page]

1984
*
Mathematical Reviews
*

In this paper the authors consider a restricted family of

*random**walks*, ¢.g., p(0,x)~dx'~**with*2<a<3, drop the assumption on the third moment, and obtain a*representation*for the G‘"’( x,y). ... This*representation*,*with*eigenvalue inequalities, leads to a characterization of the*distribution*of first hitting time as the convolution or mixture of*distributions*related to the geometric. ...##
###
Page 4241 of Mathematical Reviews Vol. , Issue 88h
[page]

1988
*
Mathematical Reviews
*

Asymptotic

*representation*of the potential of a lower*continuous**random**walk*on a*Markov*chain. (Russian) Analytic methods in reliability theory (Russian), 70-75, vi, Akad. Nauk Ukrain. SSR, Inst. ... Summary (translated from the Russian): “We obtain an asymptotic*representation*of the potential of a nondegenerate integer lower*continuous**random**walk*on a*Markov*chain in the case when the mathematical ...##
###
Page 4829 of Mathematical Reviews Vol. , Issue 95h
[page]

1995
*
Mathematical Reviews
*

This paper deals

*with*the derivation of exact joint*distributions*of*random*variables that are additive functionals defined on ex- cursions of a simple symmetric*random**walk*. ...*random**walks*. ...##
###
Page 3980 of Mathematical Reviews Vol. , Issue 89G
[page]

1989
*
Mathematical Reviews
*

The

*distribution*of the time and place of first passage over a level k for a left-*continuous*lattice*random**walk*on a countable*Markov*chain is studied. ... It is proved under a mild condition that this*Markov*chain has at most one invariant*distribution*. As an application,*random**walks*on R**with*reflection at 0 are carefully studied. ...##
###
Page 6334 of Mathematical Reviews Vol. , Issue 92k
[page]

1992
*
Mathematical Reviews
*

In conjunction

*with*our discrete-time algorithm, this engenders an algorithm for construct- ing a*Markov*process*representation*for any*distribution*of con- tinuous phase-type.” 92k:60152 60310 60K25 Murthy ... “We also clarify the relation between the classes of*continuous*and discrete phase-type*distributions*, and show that O’Cinneide’s characterisation of*continuous*phase-type*distributions*is a corol- lary ...##
###
Memory effects and static disorder reduce information in single-molecule signals
[article]

2022
*
bioRxiv
*
pre-print

Toward this goal, a variety of low-dimensional models have been proposed as descriptions of single-molecule signals, including

doi:10.1101/2022.01.13.476256
fatcat:36cij7c6cvffbcnzrzjoou676i
*random**walks**with*or without conformational memory and/or*with*static or dynamics ... ) and non-*Markov*single-molecule signals and between static and dynamic disorder. ... More generally, various anomalous-diffusion-type phenomena are often interpreted in terms of*random**walks*on a network of "traps",*with*a certain*distribution*of the trap energies leading to a*distribution*...##
###
Page 4863 of Mathematical Reviews Vol. , Issue 99g
[page]

1999
*
Mathematical Reviews
*

*with*the help of a

*continuous*product.” ... Let {S,, » > 1} be a

*random*

*walk*generated by i.i.d

*random*vari- ables

*with*ES; > 0. ...

##
###
Page 2659 of Mathematical Reviews Vol. , Issue 99d
[page]

1991
*
Mathematical Reviews
*

We study a

*Markov*process*with*discrete time and*with*a phase space formed by the*continuous*configurations. ... In this case the 60J*Markov*processes 994:60079 limit*distribution*of a*Markov*chain corresponds to the limit ‘Gibbs’*distribution*on the set of*continuous*configurations. ...##
###
Page 5137 of Mathematical Reviews Vol. , Issue 81M
[page]

1981
*
Mathematical Reviews
*

Authors’ summary: “The joint

*distributions*, along*with*the gener- ating functions, of crossings of the line y=¢ and their runs are investigated for*random**walks*corresponding to (i) samples of unequal ... {imit » for ie v.Y,) 0133 BERT ar PN HBB TA et BO 5137 Using the asymptotic*representation*of potentials of a lattice ran- dom*walk*, the author finds the limit*distribution*of the jump over the level x ...##
###
Page 1407 of Mathematical Reviews Vol. 57, Issue 4
[page]

1979
*
Mathematical Reviews
*

., the authors give necessary and sufficient conditions that the

*random**walk*have a limiting uniform*distribution*over the region. ... Nauk 1977, no. 4, 23-28, The author considers a k-dimensional*random**walk*in a rectangu- lar region*with*reflecting, or partially reflecting walls. ...##
###
Page 7326 of Mathematical Reviews Vol. , Issue 2001J
[page]

2001
*
Mathematical Reviews
*

Assuming that this

*random**walk*is nonsymmetric in the sense that Eln p # Eln(1 — p), the authors prove that M has a stationary*distribution*of the form r(x)du(x) i.e., abso- lutely*continuous**with*respect ... (RS-AOS; Moscow) A*random**walk**with*an upper-*continuous*component, and the Lagrange inversion formula. (Russian. Russian summary) Teor. Veroyatnost.i Primenen. 45 (2000), no. 1, 166-175. ...##
###
Page 1493 of Mathematical Reviews Vol. , Issue 88c
[page]

1988
*
Mathematical Reviews
*

Define a right

*random**walk*on S as the product Z, = X,X2---Xn, n > 1, where the factors are independent and identically*distributed**with*law yw. ... Let S = (So, Si,---) be a*random**walk**with*S; in the domain of attraction of a stable*distribution*. Let S and S be two independent copies of S. Define M, = maxo<j<; 5S; and my = Maxg<j<;(—5Si). ...##
###
Page 4113 of Mathematical Reviews Vol. , Issue 99f
[page]

1999
*
Mathematical Reviews
*

Compactness and limit properties for the

*random**walk*model; 6. Laplace principle for the*random**walk*model*with**continuous*statistics; 7. ... Extension of the Laplace principle for the empirical measures of a*Markov*chain; 10. Laplace principle for the*continuous*time*Markov*processes*with**continuous*statistics. ...##
###
The cutoff phenomenon in finite Markov chains

1996
*
Proceedings of the National Academy of Sciences of the United States of America
*

It shows that chains

doi:10.1073/pnas.93.4.1659
pmid:11607633
pmcid:PMC39998
fatcat:kxswbudqfvetbohxy6ailuv4t4
*with*polynomial growth (drunkard's*walk*) do not show cutoffs. ... Natural mixing processes modeled by*Markov*chains often show a sharp cutoff in their convergence to long-time behavior. ... These heuristics thus predict a cutoff for*random**walks*where the size of the*representations*grow*with*the size of the group. ...
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