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Local times of additive Lévy processes

Local times of additive Lévy processes,10.1016/S0304-4149(02)00237-5,Stochastic Processes and Their Applications,Davar Khoshnevisan,Yimin Xiao,Yuquan

Local times of additive Lévy processes   (Citations: 15)
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Let X={X(t);t∈R+N} be an additive Lévy process in Rd withX(t)=X1(t1)+⋯+XN(tN)∀t∈R+N,where X1,…,XN are independent, classical Lévy processes on Rd with Lévy exponents Ψ1,…,ΨN, respectively. Under mild regularity conditions on the Ψi's, we derive moment estimates that imply joint continuity of the local times in question. These results are then refined to precise estimates for the local and uniform moduli of continuity of local times when all of the Xi's are strictly stable processes with the same index α∈(0,2].
Journal: Stochastic Processes and Their Applications - STOCH PROC APPL , vol. 104, no. 2, pp. 193-216, 2003
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    • ...Bertoin 2002 ;S ato 1999; Khoshnevisan et al. 2003),...
    • ...for all ξ ∈ R m and for a given a ∈ R m .H ereL is a finite measure on R m concentrated on R m −{ 0}. ψ is called the Lévy exponent of A and L is the corresponding Lévy measure (Khoshnevisan et al. 2003)...

    Eitan Altman. Semi-linear Stochastic Difference Equations

    • ...divisible random fields as well; see [10, 12] and [20]...
    • ...The following theorem establishes sharp H¨older conditions for the maximum local times L ∗ (T) = sup x∈Rd L(x, T) of fractional Brownian sheets as diam(T) → 0. Similar results for Brownian motion and some other random fields have been obtained by several authors. See, for example, [12, 16, 20, 30]...
    • ...As in [12, 20, 30], the proof of Theorem 4.3 is based on Lemma 3.12 and a chaining argument...

    Antoine Ayacheet al. Joint continuity of the local times of fractional Brownian sheets

    • ...Lévy exponent of A and L is the corresponding Lévy measure [33]...

    Eitan Altmanet al. Expected waiting time in symmetric polling systems with correlated wal...

    • ...We rely on two recent papers by Khoshnevisan, Xiao and Zhong [23, 24] for the constructions of the local time �x(I)...
    • ...Xiao and Zhong [23, 24] consider a more general multiparameter random field named additive L´evy process, which is generated by independent L´evy processes...
    • ...is jointly continuous in (x,t) (Corollary 3.3 of [24])...
    • ...We mention that in the stable case, Khoshnevisan, Xiao and Zhong ([24],...

    Xia Chen. LARGE DEVIATIONS AND LAWS OF THE ITERATED LOGARITHM FOR THE LOCAL TIME...

    • ...Recently, Zhong and Hu [11] studied the self-intersection local times for an additive L´ evy process, Khoshnevisan, Xiao and Zhong [12] considered the...

    Rongmao Zhanget al. Some path properties of generalized Lévy sheet

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