Functional limit theorems for random walks perturbed by positive alpha-stable jumps
نویسندگان
چکیده
Let ξ1, ξ2,… be i.i.d. random variables of zero mean and finite variance η1, η2,… positive whose distribution belongs to the domain attraction an α-stable distribution, α∈(0,1). The two collections are assumed independent. We consider a Markov chain with jumps types. If present position is positive, then jump ξk occurs; if nonpositive, ηk occurs. prove functional limit theorems for this closely related chains under Donsker’s scaling. weak nonnegative process (X(t))t≥0 satisfying stochastic equation dX(t)=dW(t)+dUα(LX(0)(t)), where W Brownian motion, Uα subordinator which independent W, LX(0) local time X at 0. Also, we explain that Feller motion ‘jump-type’ exit from
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ژورنال
عنوان ژورنال: Bernoulli
سال: 2023
ISSN: ['1573-9759', '1350-7265']
DOI: https://doi.org/10.3150/22-bej1515