Related papers: Affine Volterra processes
This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations…
Local Fourier analysis is a commonly used tool to assess the quality and aid in the construction of geometric multigrid methods for translationally invariant operators. In this paper we automate the process of local Fourier analysis and…
We consider a stochastic factor financial model where the asset price process and the process for the stochastic factor depend on an observable Markov chain and exhibit an affine structure. We are faced with a finite time investment horizon…
We develop precise bounds on the growth rates and fluctuation sizes of unbounded solutions of deterministic and stochastic nonlinear Volterra equations perturbed by external forces. The equation is sublinear for large values of the state,…
We carry out the generalization of the Lotka-Volterra embedding to flows not explicitly recognizable under the Generalized Lotka-Volterra format. The procedure introduces appropiate auxiliary variables, and it is shown how, to a great…
We discuss the pricing and hedging of volatility options in some rough volatility models. First, we develop efficient Monte Carlo methods and asymptotic approximations for computing option prices and hedge ratios in models where…
We reexamine the problem of having nonconservative equations of motion arise from the use of a variational principle. In particular, a formalism is developed that allows the inclusion of fractional derivatives. This is done within the…
We implement a new semi-analytical approach to investigate radially self-similar solutions for the steady-state advection-dominated accretion flows (ADAFs). We employ the usual $\alpha$-prescription for the viscosity and all the components…
The paper focuses on solving one class of Volterra equations of the first kind, which is characterized by the variability of all integration limits. These equations were introduced in connection with the problem of identifying nonsymmetric…
We study a class of degenerate convection diffusion equations with a fractional nonlinear diffusion term. These equations are natural generalizations of anomalous diffusion equations, fractional conservations laws, local convection…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine the weakly singular nature of this convolution…
In this paper we consider a broad class of infinite horizon discrete-time optimal control models that involve a nonnegative cost function and an affine mapping in their dynamic programming equation. They include as special cases classical…
Motivated by the traditional Lotka-Volterra competitive models, this paper proposes and analyzes a class of stochastic reaction-diffusion partial differential equations. In contrast to the models in the literature, the new formulation…
Variable-exponent fractional models attract increasing attentions in various applications, while the rigorous analysis is far from well developed. This work provides general tools to address these models. Specifically, we first develop a…
In the paper, we improve our earlier results concerning the existence, uniqueness and differentiability of a global implicit function. Some application to a Cauchy problem for an integro-differential Volterra system of nonconvolution type,…
In this paper we characterise the Lp stability of perturbed linear Volterra integrodifferential convolution equations. Additionally we provide a framework which points to necessary and sufficient conditions on the forcing function that…
For a generalized scale function of standard processes, we characterize it as a unique solution to a Volterra type integral equation. This allows us to extend it to an entire function and to derive a useful identity that we call the…
The aim of this note is to provide some results for stochastic convolutions corresponding to stochastic Volterra equations in separable Hilbert space. We study convolution of the form $W^{\Psi}(t):=\int_0^t S(t-\tau)\Psi(\tau)dW(\tau)$,…
The well-posedness is established for multi-dimensional mean-field stochastic Volterra equations with Lipschitz continuous coefficients and allowing for singular kernels as well as for one-dimensional mean-field stochastic Volterra…