Limit theorems for trawl processes
Copyright policy )Limit theorems for trawl processes
In this work we derive limit theorems for trawl processes. First,we study the asymptotic behaviour of the partial sums of the discretized trawl process $(X_{i��_{n}})_{i=0}^{\lfloor nt\rfloor-1}$, under the assumption that as $n\uparrow\infty$, $��_{n}\downarrow0$ and $n��_{n}\rightarrow��\in[0,+\infty]$. Second, we derive a functional limit theorem for trawl processes as the L��vy measure of the trawl seed grows to infinity and show that the limiting process has a Gaussian moving average representation.
35 pages
- Sorbonne University France
- Sorbonne Paris Cité France
- Imperial College London United Kingdom
- SORBONNE UNIVERSITÉ France
- University of Toronto Canada
570, Statistics & Probability, functional limit theorem, Trawl process, trawl process, Processes with independent increments; Lévy processes, math.PR, moving average, 510, partial sum, Moving average, Stationary stochastic processes, FOS: Mathematics, Partial sum, Stable convergence, 0105 Mathematical Physics, Functional limit theorems; invariance principles, 0104 Statistics, Probability (math.PR), Fractional processes, including fractional Brownian motion, Functional limit theorem, Brownian motion, stable convergence, Mathematics - Probability, Random measures
570, Statistics & Probability, functional limit theorem, Trawl process, trawl process, Processes with independent increments; Lévy processes, math.PR, moving average, 510, partial sum, Moving average, Stationary stochastic processes, FOS: Mathematics, Partial sum, Stable convergence, 0105 Mathematical Physics, Functional limit theorems; invariance principles, 0104 Statistics, Probability (math.PR), Fractional processes, including fractional Brownian motion, Functional limit theorem, Brownian motion, stable convergence, Mathematics - Probability, Random measures
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