Matches in SemOpenAlex for { <https://semopenalex.org/work/W2949602746> ?p ?o ?g. }
Showing items 1 to 60 of
60
with 100 items per page.
- W2949602746 abstract "Random walks in random scenery are processes defined by $Z_n:=sum_{k=1}^nxi_{X_1+...+X_k}$, where basically $(X_k,kge 1)$ and $(xi_y,yinmathbb Z)$ are two independent sequences of i.i.d. random variables. We assume here that $X_1$ is $ZZ$-valued, centered and with finite moments of all orders. We also assume that $xi_0$ is $ZZ$-valued, centered and square integrable. In this case H. Kesten and F. Spitzer proved that $(n^{-3/4}Z_{[nt]},tge 0)$ converges in distribution as $nto infty$ toward some self-similar process $(Delta_t,tge 0)$ called Brownian motion in random scenery. In a previous paper, we established that ${mathbb P}(Z_n=0)$ behaves asymptotically like a constant times $n^{-3/4}$, as $nto infty$. We extend here this local limit theorem: we give a precise asymptotic result for the probability for $Z$ to return to zero simultaneously at several times. As a byproduct of our computations, we show that $Delta$ admits a bi-continuous version of its local time process which is locally Holder continuous of order $1/4-delta$ and $1/6-delta$, respectively in the time and space variables, for any $delta>0$. In particular, this gives a new proof of the fact, previously obtained by Khoshnevisan, that the level sets of $Delta$ have Hausdorff dimension a.s. equal to 1/4. We also get the convergence of every moment of the normalized local time of $Z$ toward its continuous counterpart." @default.
- W2949602746 created "2019-06-27" @default.
- W2949602746 creator A5011717471 @default.
- W2949602746 creator A5018690406 @default.
- W2949602746 creator A5040935983 @default.
- W2949602746 creator A5089440305 @default.
- W2949602746 date "2014-01-01" @default.
- W2949602746 modified "2023-09-27" @default.
- W2949602746 title "On the local time of random processes in random scenery" @default.
- W2949602746 cites W1529466478 @default.
- W2949602746 cites W1542912597 @default.
- W2949602746 cites W1575826768 @default.
- W2949602746 cites W2023029053 @default.
- W2949602746 cites W2046308786 @default.
- W2949602746 cites W2078766528 @default.
- W2949602746 cites W2086423633 @default.
- W2949602746 cites W2487396901 @default.
- W2949602746 cites W2963070788 @default.
- W2949602746 cites W2125444888 @default.
- W2949602746 hasPublicationYear "2014" @default.
- W2949602746 type Work @default.
- W2949602746 sameAs 2949602746 @default.
- W2949602746 citedByCount "0" @default.
- W2949602746 crossrefType "journal-article" @default.
- W2949602746 hasAuthorship W2949602746A5011717471 @default.
- W2949602746 hasAuthorship W2949602746A5018690406 @default.
- W2949602746 hasAuthorship W2949602746A5040935983 @default.
- W2949602746 hasAuthorship W2949602746A5089440305 @default.
- W2949602746 hasBestOaLocation W29496027461 @default.
- W2949602746 hasConcept C121332964 @default.
- W2949602746 hasConcept C121864883 @default.
- W2949602746 hasConcept C33923547 @default.
- W2949602746 hasConcept C41008148 @default.
- W2949602746 hasConceptScore W2949602746C121332964 @default.
- W2949602746 hasConceptScore W2949602746C121864883 @default.
- W2949602746 hasConceptScore W2949602746C33923547 @default.
- W2949602746 hasConceptScore W2949602746C41008148 @default.
- W2949602746 hasLocation W29496027461 @default.
- W2949602746 hasLocation W29496027462 @default.
- W2949602746 hasLocation W29496027463 @default.
- W2949602746 hasLocation W29496027464 @default.
- W2949602746 hasLocation W29496027465 @default.
- W2949602746 hasLocation W29496027466 @default.
- W2949602746 hasLocation W29496027467 @default.
- W2949602746 hasOpenAccess W2949602746 @default.
- W2949602746 hasPrimaryLocation W29496027461 @default.
- W2949602746 hasRelatedWork W1974891317 @default.
- W2949602746 hasRelatedWork W2044189972 @default.
- W2949602746 hasRelatedWork W2061531152 @default.
- W2949602746 hasRelatedWork W2069964982 @default.
- W2949602746 hasRelatedWork W2313400459 @default.
- W2949602746 hasRelatedWork W2748952813 @default.
- W2949602746 hasRelatedWork W2899084033 @default.
- W2949602746 hasRelatedWork W2965437270 @default.
- W2949602746 hasRelatedWork W4225152035 @default.
- W2949602746 hasRelatedWork W4245490552 @default.
- W2949602746 isParatext "false" @default.
- W2949602746 isRetracted "false" @default.
- W2949602746 magId "2949602746" @default.
- W2949602746 workType "article" @default.