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.
Salisbury,Uniqueness for Volterra-type stochastic integral equations, ArXiv preprint arXiv:1502.05513 (2015)
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We study uniqueness for a class of Volterra-type stochastic integral equations. We focus on the case of non-Lipschitz noise coefficients. The connection of these equations to certain degenerate stochastic partial differential equations plays a key role.
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math.PR 3verdicts
UNVERDICTED 3representative citing papers
Existence of weak solutions is established for distribution-dependent stochastic Volterra equations via a local martingale problem under linear growth and mild kernel regularity.
Constructs unique strong solutions to singular stochastic Volterra differential equations driven by Wiener noise and examines Sobolev differentiability of the solution with respect to initial value.
citing papers explorer
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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.
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Weak solutions to distribution-dependent stochastic Volterra equations
Existence of weak solutions is established for distribution-dependent stochastic Volterra equations via a local martingale problem under linear growth and mild kernel regularity.
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On the Analysis of a Singular Stochastic Volterra Differential Equation driven by a Wiener Noise
Constructs unique strong solutions to singular stochastic Volterra differential equations driven by Wiener noise and examines Sobolev differentiability of the solution with respect to initial value.