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Thin points of certain Markov processes with jumps

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Automatisierte Medienanalyse

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you know that turns but thing that Battle of the Bands the other thing going on so thank you 4 thank you for all the organizers so fast John Bosco saline 18 shops and thank you for being here for 2 listen to me I'm going to talk about a strong word this minus a provider of statements at contained in France the topic is about the regularity properties of some run members sit around and talk about it at another conference for young people some glad to read talk it through to all these 2 2 2 2 2 some the young people that up the know yet so it's a good occasion the this impossible of a class of market processes is dropped the basic problem is is is the falling so let us consider of continuous time run the stochastic processes are indeed so X In 0 1 the letter defined the obligation Meyer of this process which is separately the time spent by this process at any fixed Maribel setting already so the question is the regularity of all this matter this run In the 1st the director the ruling the most basic question is is the absolute continuation of this matter so in In and moderate terminology is also called occupation downstage In the mock organs college context it is often called look at times so when you look time nominee we can consider another kind regularity properties for this matters it is called local dimensions so for this matter we consider a point in the in the in the support of we search for we want to observe some kind ,comma old fool them occupation narrow center at this point acts it is simpler than the positive room number age such as they have this relation of it is the 1st of what is not always what we find cause this limit economic may not exist and under another observation is that follow some simple for many in that happened that this explanation age may depend on the position of this act so
L give some examples the 1st example most interesting opposite can most interesting on burning motion it started this as it is now well it has been spending so many consider the local conditions this summer local time under a new mission 1 does exist and the higher dimensions the run motions and men's there's not a lot times when we consider local dimensions as adamant as the isolated up as defined in the last quarter some Protestant platter and consider have has proved that for all the points in support of this matter um running motion has local dimension to as such postings 1st the delineates the limit Lovelock limited doesn't is the 2nd thing is that for all .period the the regularity exponent of Asia is the same for all the texts so full the full of another kind the protease is a special case of process on others possibly process for example increasing stable in the process also calls pollinators office they was monitors we can also considers expression to occupation Maris local dimension of In this case not for all acts the support but for me almost every point support this is a result when Qatar India late nighties so does their interviews express exceptional SES exceptional .period so a quick answer is yes and talk about this later on the Net as just mentioned not a related question the full running motion hiring nations that don't have look at times but under the local dimension is he said is is is a constant for the point but we can consider some summer some fluctuation for the regularity of this matter uh This Modern Love erased some earlier make order so this is this is the work in the in the early after 2 solid the frequency a check paper by the new powers Rosen's between OK To the framework is the idea that I could adopt to consider his problem is a Somali fractal analysis and they got the best and the goal of this of this framework is to distinguish different local the area of the of the of the mayor consider measure of this bad description of a set points where but given regularity exponents starts with a given Powell age this quite so that the the definition would make sense always made sense is the opera local dimension where are you instead of taking them intimate taking this mindset for this long logic quantity we can always welcome come because we can also defined as lower local dimension which is only the beginning here under the American we call it a local image OK so the definition of this summer 1 of you will recall opera motif fractal special is matching 2 after associated each value of age possible age Powell too the .period dimension of this that was set for this regularity exponent but it's a lot measures just OK is a byword a is describes the whole thing of setting up the new matrix based in all this is the right notion in this contacts and the many orders and that but we can also consider for example packing dimensions of this kind of stuff look at so finally what is called .period the same .period recorded full of stable born in Asia full New almost every point that this horrible this also In this case the power law exists the limit is used for almost every point and but there are many other points we have another the tolerable With meager excellent age In this case are power to age is much smaller 2 that 1 so we call it in this case we call this the .period acts assumed .period 1 clarinetist proof that the host of dimensional 7 points misgiving regularity age Is this function so if I joint picture Of these this spectrum only lenders this is the host of the National Theatre the SAT insists that all possible value of age and other valuables Laura than to all lost more than all of our if as the host of this all simple empties can this offer corresponds to the host of the mention of the top of the range of stable so with to monitor just that give a few words on the process started the so the goal is to move to this crime scene .period care of the author John effusions junking Estes by using the notions of someone announces this is the kind of different difficulty differences stopped me on the phone for this kind of more general market processing of stationary increment of the business of being the difference between prices are stunning it also went the definition of the definition of this kind of process given by best introduced as in the late eighties and this is a market process was generate from this kind we remarked that if they is a constant function lyrics ,comma what we call off for stable despite nature of costly here we only keep the reality of the year and the large the La drafted does not influence the depressed the the simple past properties of a process what is more it OK so that as the 1st
find by this process is is this :colon it Is recognizes the casting is because in respect to some Paulson plant process focus and Paulson naira generated by possum .period process was this often this intensity I did so let us remember that we want to study the the the hostile dimension of this side of singularities so need a translation from this formulation and the way true to computer to do the competition look so the 1st saying that rely on them and then we can say is that we consider it .period acts in support of this matter this follows Marra is just the rent of this process with some closed with his they consider appointing the in the in the support we can series quantity will consider planted in the the set with this project so the solution is needed at age minus edition shown sold for even minor scales can you 0 we have this inequality it is the best describes this the time spent by this process and inside the ball with his radio spot on it is it is offered wanted by something like this and news that the process cannot be too slow so this would translate into the incremental process and it is a means that it was an increment Of the process is larger than the increment power to some 1 over age essentially not employed by Baker OK so when a son increments which means something from his estimates to do and for other connotations for the 2nd
case estimated is is the following if we consider increment this is not exactly the increment of our process and but that increment truncated large nigger nigger and 2 near under then the the the the planning firm and power to 1 lower Delta Is a truncated or large amounts officer of a certain scale then we have this uniform control for the uniform control for increment of the process and a lotta Johnson's on a much smaller to control once we have this we can kill good estimate for this
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conclusion is that the US to Laura Johnson said time t I said such that and for every empty assess the should satisfied as foreign controls configuration he signed it look so if we all this kind of double John configuration let me when we did for the for the for the for the for the population from the population that can be considered at the scale of the plant the increment of the the the intervals Miss this kind of configuration under can by considering his descendants also consider all we also truth to cheat on his stomach on configuration will get us out of freckles have and this is where given enough about the this .period remind that we do not want to computer desk cost mission the only effective wanted considered that the set of acts such as takes this is this regularity age so that there's still some staff from time to space but in this case we have with the women need now is an analog of mission doubling serum fulfill brand motion OK law analysis must win was not going to talk about it it is it concerns the construction consensus is that this on levels and the singularity so the result is following the opera multi-front respectful of this matter Is this the source of the infection is of running matching enriches the superposition of the of all this kind of this kind of curves gives also run in front of the securitization that's not
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Betrag <Mathematik>
Gesetz <Physik>
Gerichteter Graph
Deskriptive Statistik
Stetige Abbildung
Gruppe <Mathematik>
Translation <Mathematik>
Analytische Fortsetzung
Kategorie <Mathematik>
Stochastische Differentialgleichung
Translation <Mathematik>
Ordnung <Mathematik>
Klasse <Mathematik>
Mathematische Logik
Delisches Problem
Aussage <Mathematik>
Brownsche Bewegung
Prozess <Physik>
Prozess <Physik>
Regulärer Graph
Superposition <Mathematik>
Arithmetischer Ausdruck
Regulärer Graph
Uniforme Struktur
Motiv <Mathematik>
Zentrische Streckung
Lineares Funktional
Physikalischer Effekt
Abstimmung <Frequenz>
Arithmetisches Mittel
Funktion <Mathematik>
Projektive Ebene
Gewicht <Mathematik>
Obere Schranke
Prädikatenlogik erster Stufe
Inverser Limes
Leistung <Physik>
Fluktuation <Physik>
Inverser Limes
Singularität <Mathematik>


Formale Metadaten

Titel Thin points of certain Markov processes with jumps
Serientitel Les Probabilités de Demain
Teil 04
Anzahl der Teile 17
Autor Yang, Xiaochuan
Lizenz CC-Namensnennung 3.0 Unported:
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DOI 10.5446/20274
Herausgeber Institut des Hautes Études Scientifiques (IHÉS)
Erscheinungsjahr 2016
Sprache Englisch

Inhaltliche Metadaten

Fachgebiet Mathematik
Abstract A point in the state space of a stochastic process is called “thin” if the associated occupation measure of the ball centered at this point is exceptionally small. We consider in this talk the Hausdorff dimension of thin points of a class of Markov processes with jumps. This is a joint work with Stéphane Seuret.

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