Proves finite moments E[S_T^p] < ∞ for p < p_ρ in rough Bergomi under ρ ∈ [-1,0) and positive atom at zero for rough Heston variance process.
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For regular Volterra kernels the square-root process obeys a time-dependent Feller condition and stays positive; for rough regularly-varying kernels it hits zero with positive probability and carries an atom at the boundary.
Develops a Hilbert space-valued Markovian lift framework for stochastic Volterra equations and establishes existence of limit distributions, LLN with convergence rate, and CLT for time averages in the Gaussian domain.
citing papers explorer
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Moments in Rough Bergomi and Boundary Attainment in Rough Heston
Proves finite moments E[S_T^p] < ∞ for p < p_ρ in rough Bergomi under ρ ∈ [-1,0) and positive atom at zero for rough Heston variance process.
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Boundary behaviour of the Volterra square-root process
For regular Volterra kernels the square-root process obeys a time-dependent Feller condition and stays positive; for rough regularly-varying kernels it hits zero with positive probability and carries an atom at the boundary.
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Limit theorems for stochastic Volterra processes
Develops a Hilbert space-valued Markovian lift framework for stochastic Volterra equations and establishes existence of limit distributions, LLN with convergence rate, and CLT for time averages in the Gaussian domain.