Related papers: Large and moderate deviations for stochastic Volte…

In this paper, we present sufficient conditions and criteria to establish the large and moderate deviation principle of multivalued McKean-Vlasov stochastic differential equation by means of the weak convergence method.

We study multidimensional stochastic volatility models in which the volatility process is a positive continuous function of a continuous multidimensional Volterra process that can be not self-similar. The main results obtained in this paper…

We establish a comprehensive sample path large deviation principle (LDP) for log-processes associated with multivariate time-inhomogeneous stochastic volatility models. Examples of models for which the new LDP holds include Gaussian models,…

We obtain general weak existence and stability results for stochastic convolution equations with jumps under mild regularity assumptions, allowing for non-Lipschitz coefficients and singular kernels. Our approach relies on weak convergence…

This paper investigates the limit distribution of discretization errors in stochastic Volterra equations (SVEs) with general multidimensional kernel structures. While prior studies, such as Fukasawa and Ugai (2023), were focused on…

The existence of weak solutions is established for stochastic Volterra equations with time-inhomogeneous coefficients allowing for general kernels in the drift and convolutional or bounded kernels in the diffusion term. The presented…

Based on the notion of paracontrolled distributions, we provide existence and uniqueness results for rough Volterra equations of convolution type with potentially singular kernels and driven by the newly introduced class of convolutional…

In this paper, we prove the moderate deviations principle (MDP) for a general system of slow-fast dynamics. We provide a unified approach, based on weak convergence ideas and stochastic control arguments, that cover both the averaging and…

We study stochastic volatility models in which the volatility process is a positive continuous function of a continuous Volterra stochastic process. We state some pathwise large deviation principles for the scaled log-price.

In this paper, we establish a moderate deviation principle for two-dimensional stochastic Navier-Stokes equations driven by multiplicative $L\acute{e}vy$ noises. The weak convergence method introduced by Budhiraja, Dupuis and Ganguly in…

The existence of strong solutions and pathwise uniqueness are established for one-dimensional stochastic Volterra equations with locally H{\"o}lder continuous diffusion coefficients and sufficiently regular kernels. Moreover, we study the…

We introduce time-inhomogeneous stochastic volatility models, in which the volatility is described by a nonnegative function of a Volterra type continuous Gaussian process that may have very rough sample paths. The main results obtained in…

We study Euler-type discrete-time schemes for the rough Heston model, which can be described by a stochastic Volterra equation (with non-Lipschtiz coefficient functions), or by an equivalent integrated variance formulation. Using weak…

In this paper, we established a large deviation principle for stochastic models of incompressible second grade fluids. The weak convergence method introduced by \cite{Budhiraja-Dupuis} plays an important role.

We prove strong existence and uniqueness, and H\"older regularity, of a large class of stochastic Volterra equations, with singular kernels and non-Lipschitz diffusion coefficient. Extending Yamada-Watanabe's theorem, our proof relies on an…

Motivated by applications in physics (e.g., turbulence intermittency) and financial mathematics (e.g., rough volatility), this paper examines a family of integrated stochastic Volterra processes characterized by a small Hurst parameter…

We prove the existence of weak solutions for distribution-dependent stochastic Volterra equations under linear growth and continuity conditions on the coefficients and mild regularity assumptions on the kernels, including singular kernels.…

We develop a variant of rough path theory tailor-made for analyzing a class of financial asset price models known as rough volatility models. As an application, we prove a pathwise large deviation principle (LDP) for a certain class of…

We discuss the application of multistep collocation methods to Volterra integral equations which contain a weakly singular kernel $(t-\tau)^{\alpha-1}$ with $0 <\alpha <1.$ Convergence orders of the methods are determined and their…

In this paper, we first establish the existence, uniqueness and H\"older continuity of the solution to stochastic Volterra integral equations with weakly singular kernels. Then, we propose a $\theta$-Euler-Maruyama scheme and a Milstein…